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## Exterior Domains (exterior + domain)
## Selected Abstracts## Thorough analysis of the Oseen system in 2D exterior domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2009KoniecznyAbstract We construct Lp -estimates for the inhomogeneous Oseen system studied in a two-dimensional exterior domain , with inhomogeneous slip boundary conditions. The kernel of the paper is a result for the half space ,. Analysis of this model system shows us a parabolic character of the studied problem, resulting as an appearance of the wake region behind the obstacle. Main tools are given by the Fourier analysis to obtain the maximal regularity estimates. The results imply the solvability for the Navier,Stokes system for small velocity at infinity. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Local energy decay for linear wave equations with non-compactly supported initial data MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2004Ryo IkehataAbstract A local energy decay problem is studied to a typical linear wave equation in an exterior domain. For this purpose, we do not assume any compactness of the support on the initial data. This generalizes a previous famous result due to Morawetz (Comm. Pure Appl. Math. 1961; 14:561,568). In order to prove local energy decay we mainly apply two types of new ideas due to Ikehata,Matsuyama (Sci. Math. Japon. 2002; 55:33,42) and Todorova,Yordanov (J. Differential Equations 2001; 174:464). Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Attractor of dissipative radially symmetric Zakharov equations outside a ball MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2004Yongsheng LiAbstract In this paper the authors study the long time behaviour of the radially symmetric solutions to the damped Zakharov equations on an exterior domain outside a ball and prove the existence of global attractors. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Local energy decay for a class of hyperbolic equations with constant coefficients near infinity MATHEMATISCHE NACHRICHTEN, Issue 5 2010Shintaro AikawaAbstract A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial vari¬able coefficients. We shall deal with this equation in an N -dimensional exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data and the equation includes anisotropic variable coefficients {ai(x): i = 1, 2, ,, N }, which are not necessarily equal to each other (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Energy decay for the wave equation with boundary and localized dissipations in exterior domains MATHEMATISCHE NACHRICHTEN, Issue 7-8 2005Jeong Ja BaeAbstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain , with the boundary ,, = ,0 , ,1, ,0 , ,1 = ,. We impose the homogeneous Dirichlet condition on ,0 and a dissipative Neumann condition on ,1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary ,0. Under these assumptions we derive an energy decay like E(t) , C(1 + t),1 and some related estimates. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## High order boundary integral methods forMaxwell's equations using Microlocal Discretization and Fast Multipole Methods PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007E. DarrigrandAn efficient method to solve time harmonic Maxwell's equations in exterior domain for high frequencies is obtained by using the integral formulation of Després combined with a coupling method (MLFMD) based on the Microlocal Discretization method (MD) and the Multi-Level Fast Multipole Method (MLFMM) [1]. In this paper, we consider curved finite elements of higher order in the MLFMD method. Moreover, we improve the MLFMD method by sparsifying the translation matrix of the MLFMM, which involves privileged directions in that application. This improvement leads to a significant reduction of the algorithm complexity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Coupling of mapped wave infinite elements and plane wave basis finite elements for the Helmholtz equation in exterior domains INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2003Rie SugimotoAbstract The theory for coupling of mapped wave infinite elements and special wave finite elements for the solution of the Helmholtz equation in unbounded domains is presented. Mapped wave infinite elements can be applied to boundaries of arbitrary shape for exterior wave problems without truncation of the domain. Special wave finite elements allow an element to contain many wavelengths rather than having many finite elements per wavelength like conventional finite elements. Both types of elements include trigonometric functions to describe wave behaviour in their shape functions. However the wave directions between nodes on the finite element/infinite element interface can be incompatible. This is because the directions are normally globally constant within a special finite element but are usually radial from the ,pole' within a mapped wave infinite element. Therefore forcing the waves associated with nodes on the interface to be strictly radial is necessary to eliminate this internode incompatibility. The coupling of these elements was tested for a Hankel source problem and plane wave scattering by a cylinder and good accuracy was achieved. This paper deals with unconjugated infinite elements and is restricted to two-dimensional problems. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Thorough analysis of the Oseen system in 2D exterior domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2009KoniecznyAbstract We construct Lp -estimates for the inhomogeneous Oseen system studied in a two-dimensional exterior domain , with inhomogeneous slip boundary conditions. The kernel of the paper is a result for the half space ,. Analysis of this model system shows us a parabolic character of the studied problem, resulting as an appearance of the wake region behind the obstacle. Main tools are given by the Fourier analysis to obtain the maximal regularity estimates. The results imply the solvability for the Navier,Stokes system for small velocity at infinity. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Global solvability for the Kirchhoff equations in exterior domains of dimension larger than three MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2004Taeko YamazakiAbstract We consider the unique global solvability of initial (boundary) value problem for the Kirchhoff equations in exterior domains or in the whole Euclidean space for dimension larger than three. The following sufficient condition is known: initial data is sufficiently small in some weighted Sobolev spaces for the whole space case; the generalized Fourier transform of the initial data is sufficiently small in some weighted Sobolev spaces for the exterior domain case. The purpose of this paper is to give sufficient conditions on the usual Sobolev norm of the initial data, by showing that the global solvability for this equation follows from a time decay estimate of the solution of the linear wave equation. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2004A. Nazarov, SergueAbstract The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## On the absence of eigenvalues of Maxwell and Lamé systems in exterior domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2004Sebastian BauerAbstract The arguments showing non-existence of eigensolutions to exterior-boundary value problems associated with systems,such as the Maxwell and Lamé system,rely on showing that such solutions would have to have compact support and therefore,by a unique continuation property,cannot be non-trivial. Here we will focus on the first part of the argument. For a class of second order elliptic systems it will be shown that L2 -solutions in exterior domains must have compact support. Both the asymptotically isotropic Maxwell system and the Lamé system with asymptotically decaying perturbations can be reduced to this class of elliptic systems. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Energy decay for the wave equation with boundary and localized dissipations in exterior domains MATHEMATISCHE NACHRICHTEN, Issue 7-8 2005Jeong Ja BaeAbstract We study a decay property of solutions for the wave equation with a localized dissipation and a boundary dissipation in an exterior domain , with the boundary ,, = ,0 , ,1, ,0 , ,1 = ,. We impose the homogeneous Dirichlet condition on ,0 and a dissipative Neumann condition on ,1. Further, we assume that a localized dissipation a(x)ut is effective near infinity and in a neighborhood of a certain part of the boundary ,0. Under these assumptions we derive an energy decay like E(t) , C(1 + t),1 and some related estimates. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Coupling finite difference methods and integral formulas for elliptic problems arising in fluid mechanics NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2004C. AlbuquerqueAbstract This article is devoted to the numerical analysis of two classes of iterative methods that combine integral formulas with finite-difference Poisson solvers for the solution of elliptic problems. The first method is in the spirit of the Schwarz domain decomposition method for exterior domains. The second one is motivated by potential calculations in free boundary problems and can be viewed as a numerical analytic continuation algorithm. Numerical tests are presented that confirm the convergence properties predicted by numerical analysis. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 199,229, 2004 [source] |