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Green's kernels and meso-scale approximations in perforated domains

Author: V G Mazʹi︠a︡; A B Movchan; Michael Nieves
Publisher: New York : Springer, ©2013.
Series: Lecture notes in mathematics (Springer-Verlag), 2077.
Edition/Format:   Print book : EnglishView all editions and formats
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,  Read more...
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Additional Physical Format: Online version:
Mazʹi͡a, V. G.
Green's kernels and meso-scale approximations in perforated domains.
Heidelberg ; New York : Springer, c2013
(OCoLC)849509026
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: V G Mazʹi︠a︡; A B Movchan; Michael Nieves
ISBN: 3319003569 9783319003566 9783319003573 3319003577
OCLC Number: 830366838
Description: xvii, 258 pages : illustrations (some color) ; 23 cm.
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2077.
Responsibility: Vladimir Maz'ya, Alexander Movchan, Michael Nieves.

Abstract:

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.

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