Green's kernels and mesoscale approximations in perforated domains
 Author/Creator
 Mazʹi͡a, V. G.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2013.
 Physical description
 xvii, 258 p. : ill. (some col.) ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2077.
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QA3 .L28 V.2077

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QA3 .L28 V.2077
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Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 251253) 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
 Mesoscale approximations for solutions of Dirichlet problems
 Mixed boundary value problems in multiplyperforated 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) mesoscale asymptotic approximations of physical fields in nonperiodic 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.
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Vladimir Maz'ya, Alexander Movchan, Michael Nieves.
 Series
 Lecture notes in mathematics, 00758434 ; 2077
 ISBN
 3319003569
 9783319003566
 9783319003573
 3319003577