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Green's kernels and meso-scale approximations in perforated domains / Vladimir Maz'ya, Alexander Movchan, Michael Nieves.

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Author/Creator:
Mazʹi͡a, V. G.
Language:
English.
Publication date:
2013
Imprint:
Heidelberg ; New York : Springer, c2013.
Format:
  • Book
  • xvii, 258 p. : ill. (some col.) ; 24 cm.
Bibliography:
Includes bibliographical references (p. 251-253) and indexes.
Contents:
  • Uniform asymptotic formulae for Green's functions for the laplacian in domains with small perforations
  • Mixed and Neumann boundary conditions for domains with small holes and inclusions: Uniform asymptotics of Green's kernels
  • Green's function for the Dirichlet boundary value problem in a domain with several inclusions
  • Numerical simulations based on the asymptotic approximations
  • Other examples of asymptotic approximations of Green's functions in singularly perturbed domains
  • Green's tensor of the Dirichlet boundary value problem in a domain with a single inclusion
  • Green's tensor in bodies with multiple rigid inclusions
  • Green's tensor for the mixed boundary value problem in a domain with a small hole
  • Meso-scale approximations for solutions of Dirichlet problems
  • Mixed boundary value problems in multiply-perforated domains.
Summary:
The main focus of the present text is on two topics: (a) asymptotics of Green's kernels in domains with singularly perturbed boundaries and (b) meso-scale asymptotic approximations of physical fields in non-periodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations.
Contributor:
Movchan, A. B. (Alexander B.)
Nieves, Michael.
Series:
Lecture notes in mathematics, 0075-8434 ; 2077
Lecture notes in mathematics (Springer-Verlag) 2077.
Subjects:
ISBN:
3319003569
9783319003566
9783319003573
3319003577

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