ALBERT

Description:    In this note I examine a number of statement made in Wadee and Yiatros (Z. Angew. Math. Phys. 61:565–577 2010 ) in relation to my paper mentioned in the title. Most of the claims by Drs. Wadee and Yiatros are re-examined here in the proper context and it is shown that the results of the title paper are free of any errors. Content Type Journal Article Pages 1-4 DOI 10.1007/s00033-011-0133-4 Authors Ciprian D. Coman, School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW UK Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The existence of at least one mass-conserving solution for continuous coagulation-fragmentation equation has been established by Escobedo et al. (J Differ Equ 195:143–174, 2003 ) for a large class of coagulation kernels under strong binary fragmentation. In this work, uniqueness of mass-conserving solutions is demonstrated with some additional restrictions on the fragmentation kernels. Content Type Journal Article Pages 1-17 DOI 10.1007/s00033-011-0129-0 Authors Ankik Kumar Giri, Institute for Applied Mathematics, Montan University Leoben, Franz Josef Straße 18, Leoben, 8700 Austria Gerald Warnecke, Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The initial-value problem for u t = - D 2 u - m D u - l D | Ñ u | 2 + f ( x )              ( * ) is studied under the conditions \frac ¶ ¶ n u =\frac ¶ ¶ n D u =0 on the boundary of a bounded convex domain W Ì \mathbb R n with smooth boundary. This problem arises in the modeling of the evolution of a thin surface when exposed to molecular beam epitaxy. Correspondingly the physically most relevant spatial setting is obtained when n  = 2, but previous mathematical results appear to concentrate on the case n  = 1. In this work, it is proved that when n  ≤ 3,  μ ≥ 0, λ 〉 0 and f Î L ¥ ( W ) satisfies ó õ W   f ³ 0 , for each prescribed initial distribution u 0 Î L ¥ ( W ) fulfilling ó õ W   u 0 ³ 0 , there exists at least one global weak solution u Î L 2 loc ([0, ¥ ); W 1,2 ( W )) satisfying ó õ W   u (·, t ) ³ 0 for a.e. t  〉 0, and moreover, it is shown that this solution can be obtained through a Rothe-type approximation scheme. Furthermore, under an additional smallness condition on  μ and || f || L ¥ ( W ) , it is shown that there exists a bounded set S Ì L 1 ( W ) which is absorbing for ( * ) in the sense that for any such solution, we can pick T  〉 0 such that e 2 l u (·, t ) Î S for all t  〉  T , provided that Ω is a ball and u 0 and f are radially symmetric with respect to x  = 0. This partially extends similar absorption results known in the spatially one-dimensional case. The techniques applied to derive appropriate compactness properties via a priori estimates include straightforward testing procedures which lead to integral inequalities involving, for instance, the functional ó õ W   e 2 l u dx , but also the use of a maximum principle for second-order elliptic equations. Content Type Journal Article Pages 1-34 DOI 10.1007/s00033-011-0128-1 Authors Michael Winkler, Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number ( Da *), stress jump coefficient ( β ), volume fraction ( ε ), and effective viscosity. Content Type Journal Article Pages 1-20 DOI 10.1007/s00033-011-0123-6 Authors Jai Prakash, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302 India G. P. Raja Sekhar, Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302 India Mirela Kohr, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str., 400084 Cluj-Napoca, Romania Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The authors study the small oscillations of a pendulum containing an almost homogeneous, incompressible, inviscid liquid (i.e. a liquid whose density in equilibrium is practically a linear function of the height, which differs very little from a constant) and a moving gas. Using functional analysis, they prove that the spectrum is comprised of a countable set of real eigenvalues and an essential spectrum, which fills an interval, and they give an existence and uniqueness theorem for the solution of the evolution problem. Content Type Journal Article Pages 1-20 DOI 10.1007/s00033-011-0118-3 Authors H. Essaouini, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco L. El Bakkali, Faculté des Sciences de Tétouan, Université Abdelmalek Essaâdi, Mhannech II, B.P: 2121, Tétouan, Morocco P. Capodanno, Université de Franche-Comté, 2B, Rue des jardins, 25000 Besançon, France Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We show how monotonicity methods combined with infinite dimensional sandwich pairs can be used to solve very general systems of equations that are not semibounded. Content Type Journal Article Pages 1-18 DOI 10.1007/s00033-010-0108-x Authors Martin Schechter, Department of Mathematics, University of California, Irvine, CA 92697-3875, USA Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We prove that the spherically symmetric subsonic flows in an infinitely long straight divergent nozzle with arbitrary smooth cross-section are unique for the three-dimensional steady potential flow equation. The proof depends on an extreme principle for elliptic equations in an unbounded conical domain, under the assumption that the gradient of the solution is of order O (\frac1 | x | ) as | x | ® ¥ . Similar result holds for steady subsonic Euler flows in two-dimensional infinitely long straight divergent nozzles. Content Type Journal Article Pages 1-7 DOI 10.1007/s00033-010-0107-y Authors Li Liu, Shanghai Institute of Foreign Trade, 201620 Shanghai, China Hairong Yuan, Department of Mathematics, East China Normal University, 200241 Shanghai, China Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    We produce the equations of small deformations superimposed upon large for materially uniform but inhomogeneous bodies and specialize to an isotropic material and to a homogeneous finite elastic deformation. By assuming the small deformation to be a plane wave, a set of equations for the amplitude of the wave is produced which is accompanied by an additional set of conditions. By requiring a non-trivial solution for the amplitude, we obtain the secular equation and from it a set of necessary and sufficient conditions for having a real wave speed. The second set of conditions that have to be satisfied is due to the materials inhomogeneity. Essentially, the present analysis enhances the approach of Hayes and Rivlin for materially uniform but inhomogeneous bodies. The outcome is that for such bodies the restrictions on the constitutive law for having real wave speeds for an isotropic material subjected to a pure homogeneous deformation involves the field of the inhomogeneity as well. Content Type Journal Article Pages 1-10 DOI 10.1007/s00033-011-0125-4 Authors Dimitris Sfyris, Department of Civil Engineering and Geodesy, Institute of Continuum Mechanics, Technical University of Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germany Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    The stability of anisotropic electroactive polymers is investigated. A general criterion for the onset of instabilities under plane-strain conditions is introduced in terms of a sextic polynomial whose coefficients depend on the instantaneous electroelastic moduli. In a way of an example, the stable domains of layered neo-Hookean dielectrics are determined. It is found that depending on the direction of the electrostatic excitation field relative to the lamination direction, the critical stretch ratios at which instabilities may occur can be either larger or smaller than the ones for the purely mechanical case. Content Type Journal Article Pages 1-12 DOI 10.1007/s00033-011-0136-1 Authors Stephan Rudykh, The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, 84105 Beer-Sheva, Israel Gal deBotton, The Pearlstone Center for Aeronautical Studies, Department of Mechanical Engineering, Ben-Gurion University, 84105 Beer-Sheva, Israel Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275

Description:    A new mathematical model of two-temperature magneto-thermoelasticity is constructed where the fractional order heat conduction law is considered. The state space approach is adopted for the solution of one-dimensional application for a perfect conducting half-space of elastic material with heat sources distribution in the presence of a transverse magnetic field. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory are given. Some comparisons are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter on all the studied fields. Content Type Journal Article Pages 1-16 DOI 10.1007/s00033-011-0126-3 Authors Magdy A. Ezzat, Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt Ahmed S. El Karamany, Department of Mathematical and Physical Sciences, Nizwa University, P. O. Box 1357, Nizwa, 611 Oman Journal Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Online ISSN 1420-9039 Print ISSN 0044-2275