ALBERT

Description: In this paper, we are first interested in the compressible Navier–Stokes equations with density dependent viscosities in bounded domains with non-homogeneous Dirichlet conditions. We study the well posedness of such models with density dependent viscosity coefficients in the non-stationary and in the stationary cases. We apply the last result in thin domains context, justifying the compressible Reynolds equations. Content Type Journal Article Pages 193-231 DOI 10.3233/ASY-2011-1070 Authors Laurent Chupin, Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Aubière, France Rémy Sart, Ecole Supérieure d'Ingénieurs Léonard de Vinci, Paris La Défense, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 3-4 / 2012

Description: We study the mean field limit of nonrelativistic quantum many-boson systems with delta potential in one-dimensional space. Such problem is related to the semiclassical limit of a second quantized Hamiltonian with an interaction given by a quartic Wick product. In this framework, we show that the evolution of coherent states is semiclassically given by squeezed coherent states under the action of a time-dependent affine Bogoliubov transformation. Results similar to those stated by Hepp [Comm. Math. Phys. 35 (1974), 265–277] and Ginibre-Velo [Comm. Math. Phys. 66 (1979), 37–76 and 68 (1979), 45–68] are proved. Furthermore, we show propagation of chaos for Schrödinger dynamics in the mean field limit using the argument of Rodnianski–Schlein [Comm. Math. Phys. 291 (2009), 31–61]. Thus, we provide a derivation of the cubic NLS equation in one dimension. Content Type Journal Article Pages 123-170 DOI 10.3233/ASY-2011-1064 Authors Z. Ammari, IRMAR, Université de Rennes I, UMR-CNRS 6625, Campus de Beaulieu, 35042 Rennes Cedex, France. E-mails: {zied.ammari, sebastien.breteaux}@univ-rennes1.fr S. Breteaux, IRMAR, Université de Rennes I, UMR-CNRS 6625, Campus de Beaulieu, 35042 Rennes Cedex, France. E-mails: {zied.ammari, sebastien.breteaux}@univ-rennes1.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 3-4 / 2012

Description: In this paper we consider the nonclassical initial and initial-boundary value problems for second-order evolution equations with nonlocal initial conditions. We study the existence and uniqueness, in suitable abstract spaces, of solution of vector-valued distributions for such problems. We also present an algorithm of approximation of the solution of nonclassical problem with nonlocal initial conditions by a sequence of solutions of the corresponding classical problems. As an example we investigate the case of nonclassical hyperbolic equations and systems. In this particular case we show that the existence and uniqueness of solutions rely on algebraic properties of the ratios of values of the time variable in the nonlocal initial conditions and sizes of the spatial domain. Content Type Journal Article Pages 171-192 DOI 10.3233/ASY-2011-1065 Authors G. Avalishvili, Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia M. Avalishvili, School of Mathematics and Information Technologies, University of Georgia, Tbilisi, Georgia B. Miara, Laboratoire de Modélisation et Simulation Numérique École Supérieure d'Ingénieurs en Électrotechnique et Électronique, Cité Descartes, Noisy-le-Grand Cedex, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 3-4 / 2012

Description: We consider a Schrödinger operator HA D with a non-vanishing radial magnetic field B=dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of the resolvent of this operator. Under some assumptions on an additional radial potential V the operator HA D −V has a discrete negative spectrum and we obtain an upper bound of the number of negative eigenvalues. As a consequence we get an upper bound of the number of eigenvalues of HA D smaller than any positive value λ, which involves the minimum of B and the square of the L 2 -norm of A(r)/r, where A(r) is the specific magnetic potential defined as the flux of the magnetic field through the disk of radius r centered in the origin. Content Type Journal Article Pages 233-248 DOI 10.3233/ASY-2011-1077 Authors Françoise Truc, Institut Fourier, Unité mixte de recherche CNRS-UJF 5582, BP 74, 38402 – Saint Martin d'Hères Cedex, France. E-mail: francoise.truc@ujf-grenoble.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 3-4 / 2012

Description: Using the periodic unfolding method we derive the homogenized equations for the quasi-static initial boundary value problem with internal variables, which model the deformation behavior of viscoplastic materials with a periodic microstructure. The free energy associated with the problem is allowed to be positive semi-definite. Content Type Journal Article Pages 1-29 DOI 10.3233/ASY-2012-1108 Authors Sergiy Nesenenko, Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany. Tel.: +49 6151 16 2788; E-mail: nesenenko@mathematik.tu-darmstadt.de Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 81 Journal Issue Volume 81, Number 1 / 2013

Description: We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state depending on only one variable. The direction of propagation is orthogonal to this variable, and the support is concentrated on flat strips of the stationary state. The frequencies of the solution are given by the locally constant velocities associated with the stationary state. Content Type Journal Article Pages 31-34 DOI 10.3233/ASY-2012-1117 Authors Nicolas Crouseilles, INRIA – Rennes Bretagne Atlantique, IPSO Project and IRMAR (University of Rennes 1), 35042 Rennes, France. E-mails: {Nicolas.Crouseilles, Erwan.Faou}@inria.fr Erwan Faou, INRIA – Rennes Bretagne Atlantique, IPSO Project and IRMAR (University of Rennes 1), 35042 Rennes, France. E-mails: {Nicolas.Crouseilles, Erwan.Faou}@inria.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 81 Journal Issue Volume 81, Number 1 / 2013

Description: We consider the unperturbed operator H0:=(−i∇−A) 2 +W, self-adjoint in L 2 (R 2 ). Here A is a magnetic potential which generates a constant magnetic field b〉0, and the edge potential W=W¯ is a

Description: We study, on weighted Riemannian model manifolds, well posedness of the Cauchy problem for a class of quasilinear parabolic equations with a coefficient which can be singular at infinity. We establish uniqueness or non-uniqueness of bounded solutions, under suitable assumptions on the behavior at infinity of the singular coefficient and on the Green function for the weighted Laplace–Beltrami operator. Content Type Journal Article Pages 273-301 DOI 10.3233/ASY-2012-1098 Authors Fabio Punzo, Dipartimento di Matematica ‘G. Castelnuovo’, Università di Roma ‘La Sapienza’, Piazzale A. Moro 5, I-00185 Roma, Italia. E-mail: punzo@mat.uniroma1.it Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 3-4 / 2012

Description: We study the limit of the stochastic model for two dimensional second grade fluids subjected to the periodic boundary conditions as the stress modulus tends to zero. We show that under suitable conditions on the data the whole sequence of strong probabilistic solutions (u α ) of the stochastic second grade fluid converges to the unique strong probabilistic solution of the stochastic Navier–Stokes equations. Content Type Journal Article Pages 251-272 DOI 10.3233/ASY-2012-1095 Authors Paul André Razafimandimby, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa. E-mails: prazafim@ictp.it, paul.razafim@gmail.com, sango1767@gmail.com Mamadou Sango, Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa. E-mails: prazafim@ictp.it, paul.razafim@gmail.com, sango1767@gmail.com Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 3-4 / 2012

Description: We consider the Stokes problem in a domain with holes periodically distributed with a period ε. The size of the holes is of the order of ε, a small parameter going to zero. On the boundary of the holes we prescribe a Robin-type condition depending on a parameter γ. The aim is to give the asymptotic behavior of the velocity and of the pressure of the fluid as ε goes to zero. The study for a problem of this type was done in Math. Meth. Appl. Sci. 19 (1996), 857–881, via classical homogenization methods. In this work we use the periodic unfolding method in perforated domains (see C. R. Acad. Sci. Paris, Série 1 342 (2006), 469–474; Portugaliae Mathematica 63(4) (2006), 467–496; Asymptotic Analysis 53(4) (2007), 209–235; in: Multiple Scales in Problems in Biomath., Mech., Physics and Numeric, Gakuto Int. Series, Math. Sci. App., Vol. 31, Gakkokotosho, 2009, pp. 37–68, and SIAM J. Math. Anal. 44(2) (2012), 718–760), which allows us to consider a general geometric framework. We give the limit problems corresponding to different values of γ (Darcy, Brinkmann or Stokes type problems). Content Type Journal Article Pages 229-250 DOI 10.3233/ASY-2012-1094 Authors Rachad Zaki, Khalifa University of Science, Technology and Research, P.O. Box 127788, Abu Dhabi, UAE. E-mail: rachad.zaki@kustar.ac.ae Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 3-4 / 2012

Description: We show that the variational limit of a ε-soft and thin junction problem (

Description: In this paper we consider the high frequency diffraction of electromagnetic waves by a strictly convex obstacle. We restrict ourselves to the case of an obstacle in 2D and to the diffraction of a TE or TM wave. The aim of this paper is to present simultaneously with the same notations, unknowns and special functions the boundary layer analysis of this problem with stretched variables using the intuition of the solutions and the microlocal analysis way of construction of an adapted parametrix. We concentrate on the case of diffraction, i.e. studying the representation of a creeping wave on the boundary, which occurs in the case of the study of a glancing point. We use both methods to derive the exact solution near a diffractive point, obtaining results in terms of suitable Airy functions. Content Type Journal Article Pages 347-378 DOI 10.3233/ASY-2012-1137 Authors Daniel Bouche, DAM DIF, CEA Bruyeres le Chatel, F 91297, Arpajon, France Olivier Lafitte, LAGA, Institut Galilée, University Paris 13, Villetaneuse, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 3-4 / 2012

Description: We study a parabolic problem set in a domain divided by a perforated interface. The pores alternate between an open and a closed state, periodically in time. We consider the asymptotics of the solution for vanishingly small size of the pores and time period. The interface condition prevailing in the limit is a linear relation between the flux (on either side) and the jump of the limiting solution across the interface. More exactly this behaviour only takes place when the relative sizes of the relevant geometrical and temporal parameters are connected by suitable relations. With respect to the stationary version of this problem, which is known in the literature, we demonstrate the appearance of a new admissible asymptotic standard. More in general, we describe the precise interplay between the geometrical and temporal parameters leading to the quoted interface condition. This work represents a preliminary mathematical investigation of a model of selective transport of chemical species through biological membranes. Content Type Journal Article Pages 189-227 DOI 10.3233/ASY-2012-1093 Authors Daniele Andreucci, Department of Basic and Advanced Sciences for Engineering, University of Rome Sapienza, Rome, Italy Dario Bellaveglia, Department of Basic and Advanced Sciences for Engineering, University of Rome Sapienza, Rome, Italy Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 3-4 / 2012

Description: We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain Ω⊂R N , N≥1, with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a rate r −τ , τ〉1, towards the identity. As a canonical application we show that the corresponding eigen-values do not accumulate and that by means of Eidus' limiting absorption principle a Fredholm alternative holds true. Content Type Journal Article Pages 133-160 DOI 10.3233/ASY-2012-1100 Authors Dirk Pauly, Fakultät für Mathematik, Universität Duisburg-Essen, Campus Essen, Germany. URL: http://www.uni-due.de/mathematik/ag_pauly Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: In this paper, we study the theory of orthogonal trigonometric polynomials (OTPs). We obtain asymptotics of OTPs with positive and analytic weight functions by Riemann–Hilbert approach and find that they have relations with orthogonal polynomials on the unit circle (OPUC). By the relations and the theory of OPUC, we also get four-terms recurrent formulae, Christoffel–Darboux formula and some algebraic and asymptotic properties of zeros for orthogonal trigonometric polynomials. Content Type Journal Article Pages 87-132 DOI 10.3233/ASY-2012-1096 Authors Zhihua Du, Department of Mathematics, Jinan University, Guangzhou, China. E-mail: tzhdu@jnu.edu.cn Jinyuan Du, School of Mathematics and Statistics, Wuhan University, Wuhan, China. E-mail: jydu@whu.edu.cn Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: We obtain, by exploiting Jost functions, asymptotic expansions of Green functions of perturbed Hill operators with respect to the spectral parameter around the minima of the continuous spectra. From the Green function expansions, we derive asymptotic expansions for large time of heat kernels for perturbed Hill operators. Content Type Journal Article Pages 161-187 DOI 10.3233/ASY-2012-1091 Authors Minoru Murata, Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan. E-mail: minoru3@math.titech.ac.jp Tetsuo Tsuchida, Department of Mathematics, Meijo University, Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan. E-mail: tsuchida@meijo-u.ac.jp Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: We consider a nearly-elastic model system with one degree of freedom. In each collision with the “wall”, the system can either lose or gain a small amount of energy due to stochastic perturbation. The weak limit of the corresponding slow motion, which is a stochastic process on a graph, is calculated. A large deviation type asymptotics and the metastability of the system are also considered. Content Type Journal Article Pages 65-86 DOI 10.3233/ASY-2011-1090 Authors Wenqing Hu, Department of Mathematics, University of Maryland, College Park, MD, USA. E-mail: huwenqing@math.umd.edu Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szegö-type theorem for resonance clusters showing that the limiting distribution of the resonance shifts concentrates on the classical energy surface corresponding to a rescaled eigenvalue of the hydrogen atom Hamiltonian. This result extends Szegö-type results on eigenvalue clusters to resonance clusters. There are two new features in this work: first, the study of resonance clusters requires the use of non-self-adjoint operators, and second, the Stark perturbation is unbounded so control of the perturbation is achieved using localization properties of coherent states corresponding to hydrogen atom eigenvalues. Content Type Journal Article Pages 17-44 DOI 10.3233/ASY-2011-1087 Authors Peter D. Hislop, Department of Mathematics, University of Kentucky, Lexington, KY, USA. E-mail: hislop@ms.uky.edu Carlos Villegas-Blas, Universidad Nacional Autónoma de México, Instituto de Matemáticas, Unidad Cuernavaca, Mexico. E-mail: villegas@matcuer.unam.mx Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: Let Hβ ± :=−Δ±βδ(|x|=R), be the quantum mechanical Hamiltonian describing a delta interaction living on a sphere of radius R in three dimensions, with strength β〉0. Let Dβ ± :=(−Δ+1) −1 −(Hβ ± +1) −1 and D∞ be the strong limit w.r.t. β of the operators Dβ + . For suitable sequence (βn) we prove uniform convergence of Dβn − towards D∞ with optimal rate, namely βn −1 . Convergence of the above mentioned operators against each other within Schatten–von Neumann ideals Sp, is established as well and the rate of convergence (depending on p) is determined. At the final step we discuss aspects of differences between negative and positive perturbations at large coupling. Content Type Journal Article Pages 1-15 DOI 10.3233/ASY-2011-1085 Authors Hichem BelHadjAli, Institut Préparatoire aux Etudes d'Ingénieurs de Nabeul, Nabeul, Tunisia. E-mail: hichem.belhadjali@ipein.rnu.tn Ali BenAmor, Faculty of Sciences of Gafsa, Gafsa, Tunisia. E-mail: ali.benamor@ipeit.rnu.tn Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: We consider a financial market with liquidity cost as in [Çetin, Jarrow and Protter, Finance and Stochastics 8 (2004), 311–341], where the supply function S ε (s,ν) depends on a parameter ε≥0 with S 0 (s,ν)=s corresponding to the perfect liquid situation. Using the PDE characterization of Çetin, Soner and Touzi [Finance and Stochastics 14(3) (2010), 317–341], of the super-hedging cost of an option written on such a stock, we provide a Taylor expansion of the super-hedging cost in powers of ε. In particular, we explicitly compute the first term in the expansion for a European Call option and give bounds for the order of the expansion for a European Digital Option. Content Type Journal Article Pages 45-64 DOI 10.3233/ASY-2011-1089 Authors Dylan Possamaï, CMAP, Ecole Polytechnique, Paris, France. E-mails: {dylan.possamai, nizar.touzi}@polytechnique.edu H. Mete Soner, ETH (Swiss Federal Institute of Technology), Zurich, Switzerland. E-mail: hmsoner@ethz.ch Nizar Touzi, CMAP, Ecole Polytechnique, Paris, France. E-mails: {dylan.possamai, nizar.touzi}@polytechnique.edu Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 79 Journal Issue Volume 79, Number 1-2 / 2012

Description: In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This procedure is indifferent to resonance in the eigenvalues. Moreover, we will address the writing of one component of a solution in terms of the other in the case of a planar system. Examples will be given, notably the Michaelis–Menten mechanism of enzyme kinetics. Content Type Journal Article Pages 187-215 DOI 10.3233/ASY-2011-1082 Authors Matt S. Calder, Department of Applied Mathematics, University of Western Ontario, London, ON, Canada. E-mail: mcalder9@uwo.ca David Siegel, Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada. E-mail: dsiegel@math.uwaterloo.ca Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 4 / 2012

Description: We study the Hele–Shaw–Cahn–Hilliard system that models two phase incompressible Darcian flow in porous media with matched density but arbitrary viscosity contrast. In the 3D case, we prove eventual regularity of weak solutions, as well as existence of global classical solutions if either the Péclet number is sufficiently small or the initial datum is close to one local energy minimizer of the free energy. In both 2D and 3D, we demonstrate that the ω-limit set of each trajectory consists of a single steady state. Finally, stability of local minimizers is established. Content Type Journal Article Pages 217-245 DOI 10.3233/ASY-2012-1092 Authors Xiaoming Wang, Department of Mathematics, Florida State University, Tallahassee, FL, USA. E-mail: wxm@math.fsu.edu Hao Wu, School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, China. E-mail: haowufd@yahoo.com Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 4 / 2012

Description: We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously the travelling wave profile and its propagation speed avoiding moving meshes, as we illustrate with several numerical examples. We analyze the relation of the new equation with the original one in the entire real line. We also analyze the behavior of the non-local problem in a bounded interval with appropriate boundary conditions. We show that it has a unique stationary solution which approaches the traveling wave as the interval gets larger and larger and that is asymptotically stable for large enough intervals. Content Type Journal Article Pages 145-186 DOI 10.3233/ASY-2011-1088 Authors Jose M. Arrieta, Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain. E-mail: arrieta@mat.ucm.es María López-Fernández, Institut für Mathematik. Universität Zürich, Zürich, Switzertland. E-mail: maria.lopez@math.uzh.ch Enrique Zuazua, Basque Center for Applied Mathematics, Bizkaia Technology Park, Derio, Basque Country, Spain. E-mail: zuazua@bcamath.org Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 3 / 2012

Description: In this article we study existence of boundary blow up solutions for some fractional elliptic equations including (−Δ) α u+u p =f in Ω, u=g on Ω c , lim x∈Ω,x→∂Ωu(x)=∞, where Ω is a bounded domain of class C 2 , α∈(0,1) and the functions f :Ω→R and g :R N \Ω − →R are continuous. We obtain existence of a solution u when the boundary value g blows up at the boundary and we get explosion rate for u under an additional assumption on the rate of explosion of g. Our results are extended for an ample class of elliptic fractional nonlinear operators of Isaacs type. Content Type Journal Article Pages 123-144 DOI 10.3233/ASY-2011-1081 Authors Patricio Felmer, Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, Universidad de Chile, Santiago, Chile. E-mail: pfelmer@dim.uchile.cl Alexander Quaas, Departamento de Matemática, Universidad Técnica Fedrico Santa María, Valparaíso, Chile. E-mail: alexander.quaas@usm.cl Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 3 / 2012

Description: The method of asymptotic expansions used by P.G. Ciarlet and his co-workers for justifying the two-dimensional Kirchhoff Love theory of linearly or nonlinearly elastic plates relies in a crucial way on appropriate sea lings of the components of the displacement and appropriate assumptions on the data (Lamé constants and applied forces). We give here a complete justification of these scalings and assumptions on the data in the linearized case. Content Type Journal Article Pages 47-60 DOI 10.3233/ASY-1994-9104 Authors B. Miara, Ecole Supérieure d'Ingénieurs en Electrotechnique et Electronique, Département de Mathématiques, 2, Boulevard Blaise Pascal, 93160 Noisy-Le-Grand, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 1 / 1994

Description: In this paper we study the asymptotic behavior of several classes of power-law functionals involving variable exponents pn(·)→∞, via Mosco convergence. In the particular case pn(·)=np(·), we show that the sequence {Hn} of functionals Hn:L 2 (R N )→[0,+∞] given by Hn(u)=∫R N λ(x) n /np(x)|∇u(x)| np(x)  dx   if u∈L 2 (R N )∩W 1,np(·) (R N ), +∞  otherwise, converges in the sense of Mosco to a functional which vanishes on the set u∈L 2 (R N ): λ(x)|∇u| p(x) ≤ 1 a.e. x∈R N and is infinite in its complement. We also provide an example of a sequence of functionals whose Mosco limit cannot be described in terms of the characteristic function of a subset of L 2 (R N ). As an application of our results we obtain a model for the growth of a sandpile in which the allowed slope of the sand depends explicitly on the position in the sample. Content Type Journal Article Pages 11-36 DOI 10.3233/ASY-2011-1083 Authors M. Bocea, Department of Mathematics and Statistics, Loyola University Chicago, Chicago, IL, USA. E-mail: mbocea@luc.edu M. Mihăilescu, Department of Mathematics, University of Craiova, Craiova, Romania. E-mail: mmihailes@yahoo.com M. Pérez-Llanos, Department of Mathematics, University of Texas at Austin, Austin, TX, USA. E-mail: mayte@math.utexas.edu J.D. Rossi, Departamento de Análisis Matemático, Universidad de Alicante, Alicante, Spain. E-mail: julio.rossi@ua.es Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 1-2 / 2012

Description: We study the effect of a periodic roughness on a Neumann boundary condition. We show that, as in the case of a Dirichlet boundary condition, it is possible to approach this condition by a more complex law on a domain without rugosity, called wall law. This approach is however different from that usually used in Dirichlet case. In particular, we show that this wall law can be explicitly written using an energy developed in the roughness boundary layer. The first part deals with the case of a Laplace operator in a simple domain but many more general results are next given: when the domain or the operator are more complex or with Robin–Fourier boundary conditions. Some numerical illustrations are used to obtain magnitudes for the coefficients appearing in the new wall laws. Finally, these wall laws can be interpreted using a fictive boundary without rugosity. That allows to give an application to the water waves equation. Content Type Journal Article Pages 85-121 DOI 10.3233/ASY-2011-1086 Authors Laurent Chupin, Laboratoire de Mathématiques, UMR 6620, Université Blaise Pascal, Campus des Cézeaux, F-63177 Aubière Cedex, France. E-mail: laurent.chupin@math.univ-bpclermont.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 1-2 / 2012

Description: This paper is devoted to the linear elastodynamics equations in an open bounded set with a smooth boundary in the high-frequency limit. The boundary conditions are of Dirichlet or Neumann type. Semiclassical (or Wigner) measures enable to estimate the energy density related to these equations for high frequency phenomena. We determine here the boundary conditions verified by the space–time semiclassical measures related to the elastodynamics equations for the doubly hyperbolic set (under a non-interference hypothesis on the incident semiclassical measures) and for the hyperbolic–elliptic set. The non-interference hypothesis is similar to that of L. Miller in the case of transmission problems for the wave equation. Content Type Journal Article Pages 37-83 DOI 10.3233/ASY-2011-1084 Authors Jean-Luc Akian, ONERA – The French Aerospace Lab, F-92322 Châtillon, France. Tel.: +33 1 46 73 46 41; Fax: +33 1 46 73 41 43; E-mail: jean-luc.akian@onera.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 1-2 / 2012

Description: We study a Dirichlet problem for an elliptic equation defined by a degenerate coercive operator and a singular right-hand side. We will show that the right-hand side has some regularizing effects on the solutions, even if it is singular. Content Type Journal Article Pages 1-10 DOI 10.3233/ASY-2011-1078 Authors Gisella Croce, Laboratoire de Mathématiques Appliquées du Havre, Université du Havre, 25, rue Philippe Lebon, 76063 Le Havre, France. E-mail: gisella.croce@univ-lehavre.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 78 Journal Issue Volume 78, Number 1-2 / 2012

Description: We derive the inequality ∫R|f′(x)| p h(f(x)) dx≤(\sqrt{p−1}) p ∫R(\sqrt{|f″(x)

Description: We consider an elliptic pseudo-differential equation with a highly oscillating linear potential modeled as a stationary ergodic random field. The random field is a function composed with a centered long-range correlated Gaussian process. In the limiting of vanishing correlation length, the heterogeneous solution converges to a deterministic solution obtained by averaging the random potential. We characterize the deterministic and stochastic correctors. With proper rescaling, the mean-zero stochastic corrector converges to a Gaussian random process in probability and weakly in the spatial variables. In addition, for two prototype equations involving the Laplacian and the fractional Laplacian operators, we prove that the limit holds in distribution in some Hilbert spaces. We also determine the size of the deterministic corrector when it is larger than the stochastic corrector. Depending on the correlation structure of the random field and on the singularities of the Green's function, we show that either the deterministic or the random part of the corrector dominates. Content Type Journal Article Pages 123-145 DOI 10.3233/ASY-2011-1072 Authors Guillaume Bal, Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA Josselin Garnier, Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris VII, Paris, France Yu Gu, Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA Wenjia Jing, Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 3-4 / 2012

Description: We determine the asymptotic behavior of the eigenvalues of second-order elliptic operators on finite networks under continuity and weighted Kirchhoff flow conditions at the vertices. It turns out that the quadratic growth formula in the symmetrizable case [Linear Algebra Appl. 121 (1989), 692–697; Math. Meth. Appl. Sci. 10 (1988), 383–395; Parabolic Network Equations, 2nd edn, Universitätsverlag, Tübingen, 1994] holds also in the general case when the problem cannot be reduced to a self-adjoint problem and when non-real eigenvalues occur. Content Type Journal Article Pages 147-167 DOI 10.3233/ASY-2011-1073 Authors Joachim von Below, LMPA Joseph Liouville ULCO, Université Lille Nord de France, Calais, France José A. Lubary, Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 3-4 / 2012

Description: We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a disk of radius ε and another one outside. We derive sharp estimates of the size of the scattered field caused by this disk inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tends to zero with ε. Content Type Journal Article Pages 197-246 DOI 10.3233/ASY-2011-1080 Authors Yves Capdeboscq, Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, UK. E-mail: yves.capdeboscq@maths.ox.ac.uk Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 3-4 / 2012

Description: Asymptotic expansions of solutions of the wave equations in even dimensional spaces are obtained with the initial data of non-compact support. A relationship is proved between the vanishing order at the origin of the Fourier transform of the data and the decay rate of the corresponding solutions in semi-infinite cylinders or along rays inside the forward light cone. Content Type Journal Article Pages 163-176 DOI 10.3233/ASY-1994-9205 Authors T. Ozawa, Department of Mathematics, Hokkaido University, Sapporo 060, Japan Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 2 / 1994

Description: In the lines of the recent paper [J. Amer. Math. Soc. 23(2) (2010), 591–609], we establish various ill-posedness results for the Prandtl equation. By considering perturbations of stationary non-monotonic shear flows, we show that for some C ∞ initial data, local in time H 1 solutions of the linearized Prandtl equation do not exist. At the nonlinear level, we prove that if a flow exists in the Sobolev setting, it cannot be Lipschitz continuous. Besides ill-posedness in time, we also establish some ill-posedness in space, that casts some light on the results obtained by Oleinik for monotonic data. Content Type Journal Article Pages 71-88 DOI 10.3233/ASY-2011-1075 Authors D. Gérard-Varet, Equipe d'analyse fonctionnelle, Université Denis Diderot, Institut de Mathématiques de Jussieu, Paris, France. E-mail: gerard-varet@math.jussieu.fr T. Nguyen, Equipe d'analyse fonctionnelle, Université Pierre et Marie Curie, Institut de Mathématiques de Jussieu, Paris, France. E-mail: nguyent@math.jussieu.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 1-2 / 2012

Description: The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomenon of wave packet revivals is demonstrated in this article. The framework of this paper is semi-classical analysis (limit: h→0). For the proofs we use standard tools of real analysis, Fourier analysis and basic analytic number theory. Content Type Journal Article Pages 1-41 DOI 10.3233/ASY-2011-1069 Authors Olivier Lablée, Université Grenoble 1-CNRS, Institut Fourier, UFR de Mathématiques, UMR 5582, BP 74 38402 Saint Martin d'Hères Cedex, France. E-mail: lablee@ujf-grenoble.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 1-2 / 2012

Description: We investigate the large-time behavior of viscosity solutions of quasi-monotone weakly coupled systems of Hamilton–Jacobi equations on the n-dimensional torus. We establish a convergence result to asymptotic solutions as time goes to infinity under rather restricted assumptions. Content Type Journal Article Pages 43-70 DOI 10.3233/ASY-2011-1071 Authors Hiroyoshi Mitake, Department of Applied Mathematics, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan. E-mail: mitake@hiroshima-u.ac.jp Hung V. Tran, Department of Mathematics, University of California, Berkeley, CA, USA. E-mail: tvhung@math.berkeley.edu Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 1-2 / 2012

Description: This paper is devoted to the global existence and uniqueness results for the three-dimensional Boussinesq system with axisymmetric initial data v 0 ∈B 5/2 2,1(R 3 ) and ρ 0 ∈B 1/2 2,1(R 3 )∩L p (R 3 ) with p〉6. This system couples the incompressible Euler equations with a transport-diffusion equation governing the density. In this case the Beale–Kato–Majda criterion (see [2]) is not known to be valid and to circumvent this difficulty we use in a crucial way some geometric properties of the vorticity. Content Type Journal Article Pages 89-121 DOI 10.3233/ASY-2011-1074 Authors Samira Sulaiman, IRMAR, Université de Rennes 1, Campus de Beaulieu, 35 042 Rennes cedex, France. E-mail: samira.sulaiman@univ-rennes1.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 77 Journal Issue Volume 77, Number 1-2 / 2012

Description: The paper is devoted to some foundational questions in resurgent analysis. As a main technical result, it is shown that under appropriate conditions the infinite sum of endlessly continuable majors commutes with the Laplace transform. A similar statement is proven for compatibility of a convolution and of an infinite sum of majors. We generalize the results of Candelpergher–Nosmas–Pham and prove a theorem about substitution of a small (extended) resurgent function into a holomorphic parameter of another resurgent function. Finally, we discuss an application of these results to the question of resurgence of eigenfunctions of a one-dimensional Schrödinger operator corresponding to a small resurgent eigenvalue. Content Type Journal Article Pages 87-114 DOI 10.3233/ASY-2011-1068 Authors Alexander Getmanenko, Department of Mathematics, Northwestern University, Evanston IL, USA; Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany; Institute for the Physics and Mathematics of the Universe, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8568, Japan. Fax: +81 4 7136 4941; E-mail: Alexander.Getmanenko@ipmu.jp Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 2 / 2012

Description: We consider the positive solutions u of −Δu+u−u p =0 in [0,2π]×R N−1 , which are 2π-periodic in x1 and tend uniformly to 0 in the other variables. There exists a constant C such that any solution u verifies u(x1,x′)≤Cw0(x′) where w0 is the ground state solution of −Δv+v−v p =0 in R N−1 . We prove that exactly the same estimate is true when the period is 2π/ε, even when ε tends to 0. We have a similar result for the gradient. Content Type Journal Article Pages 115-122 DOI 10.3233/ASY-2011-1076 Authors Geneviève Allain, Laboratoire d'Analyse et de Mathématiques Appliquées, Faculté de Sciences et Technologie, Université Paris-Est Créteil, Créteil, France Anne Beaulieu, Laboratoire d'Analyse et de Mathématiques Appliquées, Université Paris-Est Marne la Vallée, Marne la Vallée, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 2 / 2012

Description: We construct the weakly nonlinear-dissipative approximate system for the general compressible Navier–Stokes system in a periodic domain. It was shown in Arch. Rational Mech. Anal. 201 (2011), 377–412, that because the Navier–Stokes system has an entropy structure, its approximate system will have Leray-like global weak solutions. These solutions decompose into an incompressible part governed by an incompressible Navier–Stokes system, and an acoustic part governed by a nonlocal quadratic equation which couples it to the incompressible part. We obtain regularity results for the acoustic part of the solution via a Littlewood–Paley decomposition that extend to this general setting results found by Masmoudi [Ann. Inst. H. Poincaré 18 (2001), 199–224] and Danchin [Amer. J. Math. 124 (2002), 1153–1219] in the γ-law barotropic setting. Content Type Journal Article Pages 61-86 DOI 10.3233/ASY-2011-1066 Authors Ning Jiang, Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA. E-mail: njiang@math.tsinghua.edu.cn C. David Levermore, Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA. E-mail: lvrmr@math.umd.edu Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 76 Journal Issue Volume 76, Number 2 / 2012

Description: We prove that the resonances related to a second order elliptic differential operator with Dirichlet boundary conditions are stable in each compact of the complex plane under small C 2 -perturbations of the boundary and small changes of the coefficients. Content Type Journal Article Pages 291-296 DOI 10.3233/ASY-1994-9304 Authors P.D. Stefanov, Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 3 / 1994

Description: In this paper, we consider a sequence of integral functionals Fn:X→(−∞,+∞], where X is the set of those functions u belonging to W 1,p (0, T), p 〉 1, satisfying: u(0) = A, u(T) = B. For every n∈N,Fn is represented by the sum of two integrands, where the first one is T-periodic in time and non-convex with respect to u′ and the second one depends only on u. We give a necessary and sufficient condition in order to obtain the existence of an integral functional F∞:X→(−∞,+∞] such that, for every minimizing sequence (un) converging to u∞, the lower limit of the corresponding sequence Fn(un) coincides with F∞(u∞). The integrand function in F∞ does not depend on time and, in general, it is non-convex with respect to u′. Content Type Journal Article Pages 135-148 DOI 10.3233/ASY-1994-9203 Authors Micol Amar, Dipartimento di Matematica, Università degli Studi di Pavia, Via Abbiategrasso 209, 27100 Pavia, Italy Arrigo Cellina, S.I.S.S.A.-I.S.A.S., Via Beirut 2/4, 34014 Trieste, Italy Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 2 / 1994

Description: This paper is devoted to the mathematical analysis of some algorithms for the computation of the outgoing solution of the Helmholtz equation in an exterior domain. In a first approximation an artificial boundary with absorbing boundary condition is inserted. One then computes the periodic response in this bounded dissipative setting to a periodic forcing term. The response is characterized as the unique minimum of a convex functional. The functional is computed from solution of the time dependent problem in the artificially bounded domain. One such algorithm is due to Glowinski who proposed the functional J2 described below, it has been implemented by Bristeau et al. [5]. We propose a different functional J1 which is unconditionally coercive while the coerciveness of J2 depends in a subtle way on the geometry of the domain. It is coercive for non-trapping obstacles. The coerciveness property is essential for the convergence of the numerical method. Content Type Journal Article Pages 101-117 DOI 10.3233/ASY-1994-9201 Authors Claude Bardos, Université de Paris VII, Mathématiques, 3ème cycle, Tour 45–55, 5e etage, porte 16, 2, place Jussieu, 75251 Paris Cedex 05, France Jeffrey Rauch, Mathematics Department, University of Michigan, Ann Arbor, USA Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 2 / 1994

Description: In the first part of this study, where the linear case was considered, the appropriate scalings of the components of the displacement and the appropriate assumptions on the data (Lamé constants and applied forces) that are an essential step for deriving Kirchhoff-Love plate models by an asymptotic analysis, were justified up to a multiplicative factor. The study of the nonlinear case undertaken here, provides a full justification of this asymptotic analysis by “freezing” this dangling factor. Content Type Journal Article Pages 119-134 DOI 10.3233/ASY-1994-9202 Authors B. Miara, Ecole Supérieure d'Ingénieurs en Electrotechnique et Electronique, Département de Mathématiques, 2, Boulevard Blaise Pascal, 93160 Noisy-Le-Grand, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 2 / 1994

Description: The limit behaviour of solutions to a class of non-linear and non-local elliptic boundary value problems, with respect to the shrinking of the equivalued surface, is obtained by means of the theory of boundary value problems for second order linear elliptic equations. Content Type Journal Article Pages 297-310 DOI 10.3233/ASY-1994-9401 Authors Li Ta-Tsien, Institute of Mathematics, Fudan University, Shanghai 200433, China J.E Rodrigues, Mathematical center (CMAF), University of Lisbon, Av. Prof Gama Pinto 2, 1699 Lisbon Codex, Portugal Zhu Chen, Institute of Mathematics, Fudan University, Shanghai 200433, China Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 4 / 1994

Description: We study the dependence with respect to the domain of the constants appearing in some Sobolev embeddings. It shows that the inertial effects are negligible at the first order for the asymptotic behavior of a thin film flow. The influence of the inertial effects is obtained at the second order in the asymptotic expansions of the pressure and velocity, with full convergence argument for chosen boundary conditions. Content Type Journal Article Pages 177-208 DOI 10.3233/ASY-1994-9301 Authors Ahiko Assemien, Université Lyon I, Laboratoire d'Analyse Numérique, URA 740 CNRS, Bât. 101, 69622 Villeurbanne Cedex, France Guy Bayada, I.N.S.A., URA 856 et URA 740 CNRS, Centre de Mathématiques, Bât. 401, 69621 Villeurbanne Cedex, France Michèle Chambat, Université Lyon I, Laboratoire d'Analyse Numérique, URA 740 CNRS, Bât. 101, 69622 Villeurbanne Cedex, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 3 / 1994

Description: We study the asymptotic behaviour of the minimizers of the variational problem: min {∫ a −a[ε 2 (u′) 2 (x)+W(u(x))]dx:u∈L 1 (−a,a),u≥0,∫ a −au(x)dx=m,u(−a)=u(a)=c}, where m/2a∈(α,β) and W is a non-negative, continuous and non-convex function, with W(u) = 0 iff u∈{α,β}. We prove that the presence of the necking is related to the value c; more precisely, we have a “neck” if c〈α and a “buldge” if c〉β. Content Type Journal Article Pages 149-161 DOI 10.3233/ASY-1994-9204 Authors E. Mascolo, Istituto di Matematica “Ulisse Dini”, Università di Firenze, Viale Morgagni 67/a, 50139 Firenze, Italy L. Migliaccio, Dipartimento di Matematica e Applicazioni, Complesso Monte S. Angelo, Ed. T, Via Anzia, 80126 Napoli, Italy Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 2 / 1994

Description: We consider families of variational problems Fε over domains Ωε whose extension in one or more directions is small compared to the extension in the other directions, and goes to zero while ε tends to zero. We study then the “variational” convergence of the functionals Fε to a new functional defined on a domain A in a lower dimensional space, where those “dimensions” that were small in Ωε disappear. A general framework is presented in the first part of the paper and an application to the elastic rod and the elastic plate is given in the second part. Content Type Journal Article Pages 61-100 DOI 10.3233/ASY-1994-9105 Authors G. Anzellotti, Dipartimento di Matematica, Università degli Studi di Trento, 38050 Povo (Trento), Italy S. Baldo, Dipartimento di Matematica, Università degli Studi di Trento, 38050 Povo (Trento), Italy D. Percivale, Dipartimento di Matematica del Politecnico, Torino, Italy Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 1 / 1994

Description: We study the sum of negative eigenvalues M(h,μ) of the Schrödinger operator HV(h,μ) in L 2 (R 3 ) with a decaying at infinity potential V and a homogeneous magnetic field of intensity μ. The parameter h denotes the Planck constant. Assuming that V has a finite number of Coulomb singularities and is smooth outside them, we establish the two-term asymptotics of M(h,μ) as h→0 and μ→∞. The second term is determined only by the singularities of V and it turns out to be the same as in the case μ=0. Content Type Journal Article Pages 393-421 DOI 10.3233/ASY-1996-13404 Authors Alexander V. Sobolev, Centre for Mathematical Analysis and Its Applications, University of Sussex, Falmer, Brighton, BN1 9QH, UK. E-mail: A.V.Sobolev@sussex.ac.uk Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 13 Journal Issue Volume 13, Number 4 / 1996

Description: We consider the linear filtering problem with a small observation noise. We approximate the signal and its estimation with asymptotic expansions (see [6] and [7]). Content Type Journal Article Pages 381-395 DOI 10.3233/ASY-1994-9405 Authors Charles Marchetti, 199 avenue des Chartreux, 13004 Marseille, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 4 / 1994

Description: We consider the hyperbolic-elliptic coupled nonlinear system describing two-phase immiscible flows, with neglected capillary pressure, through a one-dimensional porous medium. We prove the existence and uniqueness of an entropy solution for data corresponding to the solution with discontinuities in saturations. Then we study the homogenization of this system when the permeability and porosity are rapidly oscillating. We get the stability of our coupled system, due to the very special underlying structure of this system in one dimension. Finally we discuss the behavior of the system with oscillatory initial saturation. This result also contains the homogenization of two-component miscible flow in a one-dimensional porous medium, without any dispersion term, as a special case. Content Type Journal Article Pages 359-380 DOI 10.3233/ASY-1994-9404 Authors Alain Bourgeat, Equipe d'Analyse Numérique, Université de Saint-Etienne, 23 rue du Docteur Paul Michelon, 42023 Saint-Etienne Cedex France Andro Mikelić, Ruder Boskovic Institute, PO Box 1016, 41001 Zagreb, Croatia Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 4 / 1994

Description: Remarks on nonminimizing solutions of a Ginzburg–Landau type equation Content Type Journal Article Pages 199-215 DOI 10.3233/ASY-1996-13204 Authors Myriam Comte Petru Mironescu Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 13 Journal Issue Volume 13, Number 2 / 1996

Description: We give some results on homogenization of transport equations involving transverse and time-dependent oscillating coefficients. For this purpose, we adapt the results of Tartar, which enable to deduce the effective equations. These latter involve memory kernels, as expected, which are described in terms of pseudodifferential operators. Other types of partial differential equations are also dealt with here, which all involve first-order time derivatives. Content Type Journal Article Pages 229-259 DOI 10.3233/ASY-1997-153-402 Authors Radjesvarane Alexandre, MAPMO, BP 6759, Université d'Orléans, F-45067, Orléans Cedex, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 15 Journal Issue Volume 15, Number 3-4 / 1997

Description: We will show how to calculate a Stokes multiplier concerning subdominant solutions of a second-order differential equation with polynomial coefficients without utilizing any suitable integral representation of its solutions. This equation is reducible to a biconfluent Huen equation. We use results of isomonodromic deformation of the differential equation. Content Type Journal Article Pages 95-107 DOI 10.3233/ASY-1996-13104 Authors Yasutaka Sibuya, School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA Tatsuhiko J. Tabara, Department of Mathematics, Golden Gate University, 536 Mission Street, San Francisco, CA 94105-2968, USA Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 13 Journal Issue Volume 13, Number 1 / 1996

Description: We study here the limit properties of the solutions of the following singular problem (1) ut−Δu+u|u| p−l =0 in R N ×R + \{(0,0)} with u(x,0)=0 if x≠(0,0). We transform the equation from an autonomous dynamical system into a weighted Sobolev space and look for the limit set of a trajectory of such a system. By using an energy method, we obtain a theorem of classification of singularities of the solutions of (1). By using the same methods we study the asymptotic behaviour of the solutions and some global singular solutions. Content Type Journal Article Pages 259-289 DOI 10.3233/ASY-1994-9303 Authors I. Moutoussamy, Département de Mathématiques, Faculté des Sciences, BP6759, 45067 Orleans Cedex 2, France L. Veron, Département de Mathématiques et Informatique Scientifique, Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 3 / 1994

Description: We consider the time dependent Schrodinger equation in the adiabatic limit when the Hamiltonian is an analytic unbounded operator. It is assumed that the Hamiltonian possesses for any time two instantaneous non-degenerate eigenvalues which display an avoided crossing of finite minimum gap. We prove that the probability of a quantum transition between these two non-degenerate eigenvalues is given in the adiabatic limit by the well-known Landau–Zener formula. Content Type Journal Article Pages 209-258 DOI 10.3233/ASY-1994-9302 Authors Alain Joye, Centre de Physique Théorique, C.N.R.S. Luminy Case 907, 13288 Marseille Cedex 9, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 3 / 1994

Description: The homogenization of non-linear elastic media and elasto-piastic media is investigated. It is shown that the results established for periodic media hold also for statistically homogeneous ergodic (S.H.E.) media. The homogenization scheme is based on (i) — a formal analogy between periodic media and S.H.E. media, and, (ii) — the study of the duality in S.H.E. non-linear media. “Explicit” direct and dual definitions of the homogenized properties are provided and illustrated by an example. Content Type Journal Article Pages 311-336 DOI 10.3233/ASY-1994-9402 Authors K. Sab, C.E.R.A.M. – Ecole Nationale des Ponts et Chaussees, Central IV, 1 Avenue Montaigne, 93167 Noisy-Le-Grand Cedex, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 4 / 1994

Description: In this paper, we study the homogenization of eigenvalue problem associated with the elasticity system in a periodically (with period ε〉0, a small parameter) perforated domain with tiny holes. The critical size of the holes aε is given by aε=C0ε N/N−2 if N≥3 and aε=exp (−C0/ε 2 ) if N=2, where C0 is a constant and N is the dimension. We will study the above eigenvalue problem as ε→0 and eigenvalues and eigenvectors. Content Type Journal Article Pages 337-358 DOI 10.3233/ASY-1994-9403 Authors A.K. Nandakumar, TIFR Centre, Post Box No. 1234, Indian Institute of Science, Bangalore 560 012, India Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 9 Journal Issue Volume 9, Number 4 / 1994

Description: In this paper, we consider the problem of pricing perpetual American put options with volatility driven by two other processes. By using a perturbation approach, we obtain approximate but explicit closed-form pricing formulae for the option and optimal exercise prices, respectively, under a general multi-scale SV (stochastic volatility) model. A key feature of the expansion methodology employed here is to balance the two SV processes, while dealing with the free boundary conditions properly. It turns out that in the current formulae, the fast volatility factor does not play an explicit role, while the slow factor is quite crucial, a phenomenon that is shown to be quite reasonable through our discussions. Content Type Journal Article Pages 133-148 DOI 10.3233/ASY-2012-1110 Authors Wen-Ting Chen, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia Song-Ping Zhu, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, Australia Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: We consider a parabolic equation with fast oscillating periodic coefficients, and an interior control in a bounded domain. First, we prove sharp convergence estimates depending explicitly on the initial data for the corresponding uncontrolled equation; these estimates are new in a bounded domain, and their proof relies on a judicious smoothing of the initial data. Then we use those estimates to prove that the original equation is uniformly null controllable, provided a carefully chosen extra vanishing interior control is added to that equation. This uniform null controllability result is the first in the multidimensional setting for parabolic equations with oscillating coefficients. Finally, we prove that the sequence of null controls converges to the optimal null control of the homogenized equation when the period tends to zero. Content Type Journal Article Pages 149-170 DOI 10.3233/ASY-2012-1111 Authors Louis Tebou, Department of Mathematics and Statistics, Florida International University, Miami, FL 33199, USA. E-mail: teboul@fiu.edu; Fax: +1 305 348 6158 Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: In this paper, we prove the existence of a uniform attractor for non-autonomous extensible beam equation with localized damping. Content Type Journal Article Pages 79-92 DOI 10.3233/ASY-2012-1106 Authors Jum-Ran Kang, Department of Mathematics, Dong-A University, Saha-Ku, Busan, Republic of Korea Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: In this paper, we study the scattering theory for a 2×2 matrix Schrödinger operator P=−h 2 d 2 /dx 2 I 2 +V(x)+hR(x,hD x ) on L 2 (R)⌖L 2 (R), where V(x) is a real diagonal matrix, the eigenvalues of which are never equal. Under some assumptions of analyticity and decay at infinity of V, we describe the asymptotic behavior of the scattering matrix S=(s ij ) 1≤i,j≤4 associated with P when the semi-classical parameter h goes to zero. Moreover, we obtain the estimate ‖S 12 ‖+‖S 21 ‖=O(e −δ/h ), where S 12 and S 21 are the two off-diagonal elements of S and δ〉0 is a constant which is explicitly related to the behavior of V(x) in the complex domain. Content Type Journal Article Pages 57-78 DOI 10.3233/ASY-2012-1105 Authors Hamadi Baklouti, Dépt de Maths, FSS, Université de Sfax, Sfax, Tunisie. E-mail: h.baklouti@gmail.com Slaheddine Ben Abdeljeilil, Dépt de Maths, FST, Université de Tunis, Tunis, Tunisie. E-mail: sabdejlil@yahoo.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: The asymptotic behaviour of a class of elliptic equations with highly oscillating coefficients, in a perforated periodic domain, is analyzed. We consider, in each period, two types of holes and we impose, on their boundaries, a Signorini and, respectively, a Neumann condition. Using the periodic unfolding method, we prove that the limit problem contains two additional terms, a right-hand side term and a “strange” one. Content Type Journal Article Pages 45-56 DOI 10.3233/ASY-2012-1104 Authors Anca Capatina, Institute of Mathematics of the Romanian Academy, Bucharest, Romania. E-mails: {anca.capatina, horia.ene}@imar.ro Horia Ene, Institute of Mathematics of the Romanian Academy, Bucharest, Romania. E-mails: {anca.capatina, horia.ene}@imar.ro Claudia Timofte, University of Bucharest, Faculty of Physics, Bucharest–Măgurele, Romania. E-mail: claudiatimofte@yahoo.com Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: In a previous work by the first author with J. Turi [Appl. Math. Optim. 58(1) (2008), 1–27], a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major advantage of the stochastic variational inequality is to overcome the need to describe the trajectory by phases (elastic or plastic). This is useful, since the sequence of phases cannot be characterized easily. In particular, when a change of regime occurs, there are numerous small elastic phases which may appear as an artefact of the Wiener process. However, it remains important to have informations on both the elastic and plastic phases. In order to reconcile these contradictory issues, we introduce an approximation of stochastic variational inequalities by imposing artificial small jumps between phases allowing a clear separation of the elastic and plastic regimes. In this work, we prove that the approximate solution converges on any finite time interval, when the size of jumps tends to 0. Content Type Journal Article Pages 171-187 DOI 10.3233/ASY-2012-1109 Authors Alain Bensoussan, International Center for Decision and Risk Analysis, School of Management, University of Texas at Dallas, Richardson, TX, USA Héctor Jasso-Fuentes, Departamento de Matemáticas, Cinvestav-IPN, México, D.F. México. E-mail: hjasso@math.cinvestav.mx Stéphane Menozzi, Université Denis Diderot-Paris 7, Paris, France. E-mail: menozzi@math.univ-paris-diderot.fr Laurent Mertz, Department of Statistics, The Chinese University of Hong Kong, Hong Kong. E-mail: mertz@sta.cuhk.edu.hk Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: We consider linear control systems of the form y′(t)=Ay(t)+Bu(t) where A generates a strongly continuous semigroup of contractions (e tA ) t≥0 on an infinite-dimensional Hilbert space Y. We suppose that the control is unbounded in the sense that the linear control operator B is bounded from the (Hilbert) control space U to some larger space W such that Y⊂W, but not from U into Y. Taking into account eventual control saturation, we study the problem of stabilization by (possibly nonlinear) monotone feedback of the form u(t)=−f(B * y(t)). We extend to the unbounded monotone feedback context weak and strong stability results which have been established for linear feedback systems. These results are based on weak observability involving the unstable subspace. This fact is illustrated by a heat equation with singular control. In the particular case where the system can be reduced to a second-order evolution equation of the form z″(t)+

Description: In this paper, we study the Dirichlet problem for an elliptic equation, in which the 1-Laplacian operator and lower-order terms appear. We introduce a suitable definition of solution and prove the existence of, at least, one bounded solution in BV(Ω) having a negligible jump part. Moreover, a uniqueness result for small positive data is proved, and explicit examples of solutions are shown. Content Type Journal Article Pages 21-43 DOI 10.3233/ASY-2012-1099 Authors Fuensanta Andreu, Departament d'Anàlisi Matemàtica, Universitat de València, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es Andrea Dall'Aglio, Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy. E-mail: dallaglio@mat.uniroma1.it Sergio Segura de León, Departament d'Anàlisi Matemàtica, Universitat de València, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: We consider systems of coupled Schrödinger equations which appear in nonlinear optics and binary Bose–Einstein condensation. Namely, we prove that for most μ,ν∈R, a,b〉0, the system −Δu=μu+au 3 −βuv 2 , −Δv=νv+bv 3 −βvu 2 , u,v∈H 1 0 (B 1 (0)), where B 1 (0) is the unit ball of R 3 , admits a family of radially symmetric positive solutions (u β ,v β ) provided the interaction parameter β〉0 is sufficiently large. By using a Morse index technique we deduce that these solutions are bounded uniformly in β, hence their limit functions as β→∞ undergo the phenomenon of phase segregation. Content Type Journal Article Pages 1-19 DOI 10.3233/ASY-2012-1097 Authors Ana Rute Domingos, CMAF – Faculty of Science, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal. Tel.: +351 217 904 911; Fax: +351 217 954 288; E-mails: {rute, mramos}@ptmat.fc.ul.pt Miguel Ramos, CMAF – Faculty of Science, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal. Tel.: +351 217 904 911; Fax: +351 217 954 288; E-mails: {rute, mramos}@ptmat.fc.ul.pt Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 1-2 / 2012

Description: We consider the Schrödinger operator with a periodic potential p on the real line. We assume that p belongs to the real Sobolev space H m on the circle for some m≥−1. We determine the sharp asymptotics of the quasimomentum and the Titchmarsh–Weyl functions, the Bloch functions at high energy. Content Type Journal Article Pages 269-287 DOI 10.3233/ASY-2012-1115 Authors Evgeny L. Korotyaev, Mathematical Physics Department, Faculty of Physics, Ulianovskaya 2, St. Petersburg State University, St. Petersburg, 198904 Russia and Pushkin Leningrad State University, Russia. E-mail: korotyaev@gmail.com Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: Let u ε be the solution of the Poisson equation in a domain periodically perforated along a manifold γ=Ω∩{x 1 =0}, with a nonlinear Robin type boundary condition on the perforations (the flux here being O(ε −κ )σ(x,u ε )), and with a Dirichlet condition on ∂Ω. Ω is a domain of R n with n≥3, the small parameter ε, that we shall make to go to zero, denotes the period, and the size of each cavity is O(ε α ) with α≥1. The function σ involving the nonlinear process is a C 1 (Ω ¯ ×R) function and the parameter κ∈R. Depending on the values of α and κ, the effective equations on γ are obtained; we provide a critical relation between both parameters which implies a different average of the process on γ ranging from linear to nonlinear. For each fixed κ a critical size of the cavities which depends on n is found. As ε→0, we show the convergence of u ε in the weak topology of H 1 and construct correctors which provide estimates for convergence rates of solutions. All this allows us to derive convergence for the eigenelements of the associated spectral problems in the case of σ a linear function. Content Type Journal Article Pages 289-322 DOI 10.3233/ASY-2012-1116 Authors D. Gómez, Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain E. Pérez, Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Santander, Spain T.A. Shaposhnikova, Department of Differential Equations, Moscow State University, Moscow, Russia Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: We study inverse scattering problems for the singular rank-one perturbations of a selfadjoint operator. We obtain a necessary and sufficient condition for a given function to be the scattering phase shift of a singular rank-one perturbation of the operator. Content Type Journal Article Pages 213-221 DOI 10.3233/ASY-2012-1112 Authors Kazushi Yoshitomi, Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minamiohsawa 1-1, Hachioji, Tokyo 192-0397, Japan. E-mail: yositomi@tmu.ac.jp Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: In this paper we derive high-order asymptotic expansions of the effective viscosity properties of a dilute periodic suspension composed of freely-suspended arbitrarily shaped particles dispersed in an incompressible Newtonian fluid. High-order terms are not only function of the viscous moment tensor but also of a distortion tensor that characterizes the periodic array. Content Type Journal Article Pages 189-211 DOI 10.3233/ASY-2012-1101 Authors Habib Ammari, Department of Mathematics and Applications, Ecole Normale Supérieure, Paris, France. E-mail: habib.ammari@ens.fr Pierre Garapon, Department of Mathematics, Stanford University, Stanford, CA, USA. E-mail: pgarapon@stanford.edu Hyeonbae Kang, Department of Mathematics, Inha University, Incheon, Korea. E-mails: {hbkang, hdlee}@inha.ac.kr Hyundae Lee, Department of Mathematics, Inha University, Incheon, Korea. E-mails: {hbkang, hdlee}@inha.ac.kr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: In this paper we introduce a PDE system which aims at describing the dynamics of a dispersed phase of particles moving into an incompressible perfect fluid, in two space dimensions. The system couples a Vlasov-type equation and an Euler-type equation: the fluid acts on the dispersed phase through a gyroscopic force whereas the latter contributes to the vorticity of the former. First we give a Dobrushin-type derivation of the system as a mean-field limit of a PDE system which describes the dynamics of a finite number of massive pointwise particles moving into an incompressible perfect fluid. This last system is itself inferred from the paper “On the motion of a small body immersed in a two-dimensional incompressible perfect fluid”, accepted for publication in Bulletin de la SMF where the system for one massive pointwise particle was derived as the limit of the motion of a solid body when the body shrinks to a point with fixed mass and circulation. Then we deal with the well-posedness issues including the existence of weak solutions. Next we exhibit the Hamiltonian structure of the system and finally, we study the behavior of the system in the limit where the mass of the particles vanishes. Content Type Journal Article Pages 53-91 DOI 10.3233/ASY-2012-1123 Authors Ayman Moussa, Laboratoire Jacques-Louis Lions, CNRS and UPMC Université Paris 06, UMR 7598, Paris, France Franck Sueur, Laboratoire Jacques-Louis Lions, CNRS and UPMC Université Paris 06, UMR 7598, Paris, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 81 Journal Issue Volume 81, Number 1 / 2013

Description: In this paper we obtain the Reynolds equation for the case of a Newtonian incompressible fluid with a stationary isothermal motion in a tribological system of radial face seals when one of the contact surfaces (the rotor) has an oscillatory motion around its equilibrium point. Moreover, it is supposed that this surface is rough. We also obtain the homogenized equation whose coefficients are given explicitly. Finally, we present numerical results for the homogenized equation. Content Type Journal Article Pages 35-52 DOI 10.3233/ASY-2012-1120 Authors Bogdan N. Nicolescu, Department of Mathematics, University of Pitesti, Pitesti, Romania. E-mails: {nicolescubogdan81, ronnytudor}@yahoo.com Tudor C. Petrescu, Department of Mathematics, University of Pitesti, Pitesti, Romania. E-mails: {nicolescubogdan81, ronnytudor}@yahoo.com Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 81 Journal Issue Volume 81, Number 1 / 2013

Description: We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of periodic coefficients. Content Type Journal Article Pages 237-267 DOI 10.3233/ASY-2012-1114 Authors Claude Le Bris, École Nationale des Ponts et Chaussées, Marne-La-Vallée, France and INRIA Rocquencourt, MICMAC Team-Project, Le Chesnay, France Frédéric Legoll, École Nationale des Ponts et Chaussées, Marne-La-Vallée, France and INRIA Rocquencourt, MICMAC Team-Project, Le Chesnay, France Florian Thomines, École Nationale des Ponts et Chaussées, Marne-La-Vallée, France and INRIA Rocquencourt, MICMAC Team-Project, Le Chesnay, France Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: In this article we prove an important inequality regarding the Ruelle operator in hyperbolic flows. This was already proven briefly by Mark Pollicott and Richard Sharp in a low dimensional case [Amer. J. Math. 120 (1998), 1019–1042], but we present a clearer proof of the inequality, filling in gaps and explaining the ideas in more detail, and extend the inequality to higher-dimensional flows. This inequality is necessary to prove a proposition about the analyticity of Ruelle zeta functions. Content Type Journal Article Pages 223-236 DOI 10.3233/ASY-2012-1113 Authors Paul Wright, School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia. E-mail: paul.e.wright@uwa.edu.au Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: We examine the decay of the energy for wave equations on a bounded domain R n , connected through one point to a rod modelled by a segment of R. It is shown that the energy decreases at least as the inverse logarithm of time. This result is obtained using a dissipative condition of the Neumann type on the boundary of the domain. Content Type Journal Article Pages 347-376 DOI 10.3233/ASY-2012-1152 Authors Leila Ouksel, Université de Paris Sud, Mathématiques, Bât. 425, 91405 Orsay Cedex, France. E-mails: Leila.Ouksel@math.u-psud.fr, louksel@yahoo.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012

Description: The aim of this paper is to extend the results obtained by Miara [Arch. Ration. Mech. Anal. 142 (1998), 331–353] and Lods and Miara [Arch. Ration. Mech. Anal. 142 (1998), 335–374] on the asymptotic analysis of nonlinearly elastic shells to the nonhomogeneous anisotropic case. To this end, we use the Hellinger–Reissner variational principle. Content Type Journal Article Pages 323-346 DOI 10.3233/ASY-2012-1119 Authors Djamal Ahmed Chacha, Laboratoire de Mathématiques Appliquées, Université Kasdi Merbah Ouargla, Ouargla, Algérie. E-mails: d_chacha@hotmail.com, miloudimath2@yahoo.fr Madjda Miloudi, Laboratoire de Mathématiques Appliquées, Université Kasdi Merbah Ouargla, Ouargla, Algérie. E-mails: d_chacha@hotmail.com, miloudimath2@yahoo.fr Journal Asymptotic Analysis Online ISSN 1875-8576 Print ISSN 0921-7134 Journal Volume Volume 80 Journal Issue Volume 80, Number 3-4 / 2012