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  • Applied Mathematics  (35)
  • Wiley-Blackwell  (35)
  • American Chemical Society
  • Periodicals Archive Online (PAO)
  • 1980-1984  (35)
  • 1965-1969
  • 1925-1929
  • 1984  (35)
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  • Wiley-Blackwell  (35)
  • American Chemical Society
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  • 1980-1984  (35)
  • 1965-1969
  • 1925-1929
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  • 1
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    Masthead (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984) 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060101
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  • 2
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    Solvability of an initial boundary value problem for the euler equations in twodimensional domain with corners (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 1-22 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The aim of this paper is to prove the existence and uniqueness of local solutions of some initial boundary value problems for the Euler equations of an incompressible fluid in a bounded domain Ω ⊂ R2 with corners. We consider two cases of a nonvanishing normal component of velocity on the boundary. In three-dimensional case such problems have been considered in papers [12], [13], [14]. Similar problems in domains without corners have been considered in [2]-[6], [11]. In this paper the relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. The paper consists of four sections. In section 1 two initial boundary value problems for the Euler equations are formulated. In section 2 the existence and uniqueness of solutions of the Laplace equation in twodimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces. In sections 3 and 4 we prove the existence and uniqueness of solutions of problems formulated in section 1, using the method of successive approximations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060102
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  • 3
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    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060104
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  • 4
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    Functional differential equations with certain monotonicity properties (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 97-103 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The present paper is concerned with the study of retarded differential equations in n-space, which satisfy some monotonicity properties. Sufficient conditions are given guaranteeing that solutions are contained in the probability (n - 1)-simplex. Existence and uniqueness of constant solutions are proved. It is also shown that every solution converges to a constant as t → ∞.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060108
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  • 5
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    On the transmission problem of the helmholtz equation for quadrantsHerrn Prof. Dr. K. Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 129-157 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The plane transmission problem of the Helmholtz equation for quadrants is characterized by a one-dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along the x-axis. It is derived by solving the transmission problem for the upper and the lower half-plane involving a Neumann condition at y = 0. This is done by a two-dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one to y = 0 then lead to the integral equation. Thereby the transmission conditions of the original problem at y = 0 have to be taken into account. The resulting integral equation is of generalized Wiener-Hopf-type. It is solved via the contraction theorem imposing restricting conditions on the wave numbers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060110
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  • 6
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    Bifurcation of periodic solutions for wave equations with scalar nonlinearities (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 206-214 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We treat wave equations with “scalar nonlinearities” and demonstrate the connection between the bifurcation theory of an associated system of Hammerstein integral equations and the existence of periodic solutions of the nonlinear wave equation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060114
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  • 7
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    Weak solutions of the initial value problem for the unmodified non-linear vlasov equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 262-279 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The existence of weak LL-solutions of the initial value problem for Vlasov's equation is proved under rather general assumptions. In the three-dimensional case the solutions exist on the entire time axis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060118
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  • 8
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    A generalized jacobi theta function (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 327-344 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The delta function initial condition solution v*(x,t;y) at x = y ≥ 0 of the generalized Feller equation is used to define a generalized Jacobi Theta function \documentclass{article}\pagestyle{empty}\begin{document}$ \Theta (x,t) = \upsilon *(x,t;0) + 2\sum\limits_{n = 1}^\infty {v*(x,t;y_n)} $\end{document} for a sufficiently rapidly increasing and unbounded positive sequence {yy}. It is shown that Θ(x,t) is analytic in each variable in certain regions of the complex x and t planes and that it is a solution of the generalized Feller equation. For those parameters for which this equation reduces to the heat equation, Θ(x,t) reduces to the third Jacobi Theta function.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060120
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  • 9
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    Applications of convex analysis and comparison functionals to extremum principles (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 353-370 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non-linear differential equation and the Fredholm integral equation.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060122
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  • 10
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    Continuous dependence on geometry for the backward heat equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we are concerned with the development of criteria for stabilizing inherently unstable initial-boundary value problems under small errors in the geometry of the underlying domain. We consider in particular the initial-boundary-value problem for the backward heat equation assuming that some error has been made in characterizing the geometry of the domain under consideration. It is shown that solutions which belong to an appropriately defined constraint set depend continuously in L2 on errors in the geometry.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060126
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  • 11
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    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060129
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  • 12
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    Two remarks on continuation procedures for solving some nonlinear equations (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 512-514 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Let F be a mapping from Rn+1 into Rn, x(t) be a parametrization for ∣t - t0 ∣ 〈 c, of a smooth solution branch of the equation F(x) = 0, A(t) be the jacobian (n + 1) associated to a standard continuation method used for computing the solution branch. We study for a class of singularities at x(t0) the behaviour, near t = t0, of the determinant of A(t).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060131
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  • 13
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    On the Vlasov-Fokker-Planck equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 527-538 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study a modification of the Vlasov-Poisson equation, obtained by adding a diffusion term with respect to velocity. It describes, from a physical point of view, a plasma in thermal equilibrium, in a mean field limit situation. We find that the already known results concerning existence and uniqueness of the solutions for the ordinary Vlasov equation (constructive results and counterexamples) translate to our case.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060134
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  • 14
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    Ein resonanzphänomen in der theorie akustischer und elektromagnetischer wellenHerrn Professor Karl Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 104-128 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We discuss the asymptotic behaviour of acoustic and electromagnetic waves, generated by given time-harmonic exterior forces with frequency ω, in the unbounded region between the parallel planes X3 = 0 and X3 = 1, and show that the principle of limiting amplitude is violated if ω = πn(n = 1, 2,…). For these values of the frequency, forces with compact support can be chosen such that the amplitudes of the waves increase with a logarithmic rate as t → ∞.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060109
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  • 15
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    Thin elastic and periodic plates (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 159-191 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e → 0 then ω → 0), (ω → 0 then e → 0) and lately (e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060112
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  • 16
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    Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 215-233 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A free boundary problem for a flow around a circle is analyzed. We find and mathematically prove that bifurcations from the trivial flow actually take place. Golubitsky-Schaeffer theory, together with a formula concerning variations of domains, enables us to clarify the behaviors of the branches of nontrivial solutions.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060115
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  • 17
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    Truncated random variables with application to random surfaces (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 248-261 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: There has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060117
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  • 18
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    Forward speed motions of a submerged body. The cauchy problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 371-392 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the linearized problem for the ideal fluid flow induced by the horizontal motion of a fully immersed body. The system of equations is made up of an elliptic problem (P) and an initialvalue problem (R) which are coupled by a pseudo-differential operator T.We define a regularized Cauchy problem (R∊) using the Yosida approximation of T; we give energy and wave resistance estimates and finally we obtain existence uniqueness and regularity of the weak solution of (R) by taking the limit when ∊ goes to zero.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060123
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  • 19
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    Half- and finite-range completeness for the equation of transfer of polarized light (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 393-416 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: On neglecting reflection by the surface the existence and uniqueness are proved for the solution of the equation of transfer of polarized light in a homogeneous semi-infinite or finite plane-parallel medium. A general LL-space formulation, where 1 ≤ p 〈 ∞, is adopted. The analysis concerns a vector-valued convolution equation, which is an equivalent form of the equation of radiative transfer and is solved with the help of Wiener-Hopf factorization, Fredholm index and cone preservation methods. The results are also proved for the equations obtained from the full equation of transfer by means of Fourier expansion and symmetry relations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060124
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  • 20
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    Exact bounds for the radially symmetric shape of confined plasma in the unit circle (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 496-511 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The method of “cone iteration”; is used to obtain exact bounds for the solutions of a class of nonlinear operator equations. The general theory is applied to the problem of finding radially symmetric solutions of the plasma problem in the unit circle. Existence and uniqueness results are obtained at the same time. Some numerical examples demonstrate the method's high degree of accuracy.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060130
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  • 21
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    Periodic motions of a string vibrating against a fixed point-mass obstacle: II (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 55-67 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A string fixed at both ends A and B, can oscillate in a plane which there is a fixed point obstacle, placed in the middle of the line AB. The string is initially at rest with a prescribed shape, symmetric with respect to the normal mid-plane of the segment AB. Using results established before [9] we find new periodic motions.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060105
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  • 22
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    Integral formulation for a steady-state transport process with general boundary conditions (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 68-83 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A linear equation for a particle steady-state transport process in a homogeneous slab of finite thickness with boundary conditions of general type is derived. This equation differs from the well-known integral equation for no-reentry boundary conditions because of the presence of a per-turbance linear operator which describes the effect of the re-emission of the particles incident at the wall. The properties of the resulting operator are investigated. The dependence of the first positive eigenvalue on physical parameters is studies in detail. The results obtained are enough to discuss the existence of a critical strictly positive solution of the physical problems which motivated this research.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060106
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  • 23
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    Scattering theory for diffraction gratings (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 158-158 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060111
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  • 24
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    Évolution quasi-statique des milieux visco-plastiques de maxwell-norton (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 192-205 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we deal with the existence and unicity of a solution of the Maxwell-Norton quasi-static problem. Some fundamental results concerning the functional spaces are first recalled. Then, by an implicit scheme, we obtain a discretized problem which is well-posed. By monotonicity techniques, we finally prove the convergence of the discrete solutions to the solution of the initial problem.
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    URL: http://dx.doi.org/10.1002/mma.1670060113
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  • 25
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    An existence theorem for compressible viscous and heat conducting fluids (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 234-247 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider an initial-boundary value problem of a flow of a viscous and heat-conducting gas in a bounded domain D ⊂ R3. We assume that the boundary S of D consists of two disjoint surfaces S1 and S2 of class C2, and that the gas enters D through the surface S1 and leaves D through the surface S2.Our aim is to prove the existence (locally in time) of a solution of the problem in anisotropic Sobolev spaces.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060116
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  • 26
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    Digitale Medien
    L2-boundary integral equations for the robin problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 345-352 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we study an integral equation method for the exterior Robin problem for the Helmholtz equation where the boundary condition is interpreted in the L2-sense. In particular, we derive a composite integral equation from Green's theorem which is uniquely solvable for all wave numbers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060121
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  • 27
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    Digitale Medien
    Some applications of a galerkin-collocation method for boundary integral equations of the first kind (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 280-325 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Here we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order - 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method using B-splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations in L2. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060119
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  • 28
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    Digitale Medien
    Exact and chapman-enskog solutions for the carleman model (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 417-432 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Chapman-Enskog procedure is applied to the Carleman model of the Boltzmann equation. It has been proved that the Carleman equations possess a solution on the time interval on which a smooth solution of the fluid-like equation exists. The calculations have been performed up to the first order i.e., to the Navier-Stokes-like equation. It has been shown that in this case a difference between an exact solution and the Chapman-Enskog solution is of order ∊2. Extension of the results to higher orders is also possible. This gives a justification of the Chapman-Enskog procedure as an asymptotic expansion method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060125
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  • 29
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    Digitale Medien
    On the geometric form of free boundaries satisfying a bernoulli condition (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 449-456 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In the x-y plane, let Ω denote an annular domain bounded by the simple closed curves ⌜ and ⌜*, such that the capacity potential U in Ω satisfies ∣ ▽ U∣ = 1 on ⌜. Assuming ⌜* to be known, we obtain qualitative properties of ⌜. For example, the number of local maxima or minima of the y-co-ordinate relative to ⌜ cannot exceed the corresponding number for ⌜*.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060127
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  • 30
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    Digitale Medien
    An error analysis of the tau method for a class of singularly perturbed problems for differential equations (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 457-466 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: By using classical results of Poincaré and Birkhoff we discuss the existence and uniqueness of solution for a class of singularly perturbed problems for differential equations. The Tau method formulation of Ortiz [6] is applied to the construction of approximate solutions of these problems. Sharp error bounds are deduced.These error bounds are applied to the discussions of a model problem, a simple one-dimensional analogue of Navier-Stokes equation, which has been considered recently by several authors (see [2], [3], [8], [10]). Numerical results for this problem [8] show that the Tau method leads to more accurate approximations than specially designed finite difference or finite element schemes.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060128
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  • 31
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    Digitale Medien
    Numerical Computation of Waves at High Frequencies by an Iterated WKB-Method (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 520-526 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An integral operator is defined, which allows to solve the equation by Neumann series for sufficiently large k 〉 0. The kernel is constructed by a modification of the WKB-method. This kernel is so simple that the operator can be used effectively for numerical calculations. Numerical results are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060133
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  • 32
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    Digitale Medien
    An approximation method for a fokker-planck-vlasov equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 23-40 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A simplified Fokker-Planck equation of statistical plasma physics is mathematically investigated. For the Cauchy problem a constructive approximation method is introduced. This procedure yields a sequence (fn) of approximate densities, uniformly converging to the problem's global classical solution with linear convergence velocity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060103
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  • 33
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    Digitale Medien
    Variational formulation of the roller contact problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 84-96 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We formulate the roller contact problem in terms of variational inequality with certain pseudodifferentional operator, and discuss a finite element technique for its numerical solution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060107
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  • 34
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    Digitale Medien
    Two classes of explicit solutions of the carleman model (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 515-519 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: For the Carleman model we show two classes of global explicit solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060132
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  • 35
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    Digitale Medien
    Local validity of the boltzmann equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 539-549 
    Details
    ISSN: 0170-4214
    Schlagwort(e): Mathematics and Statistics ; Applied Mathematics
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The validity of the Boltzmann equation is proved, locally in time, by showing that its solution is a limit of solutions of the BBGKY hierarchy.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/mma.1670060135
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