Authors:
- Systematic step-by-step approach to asymptotic algorithms that enables the reader to develop an insight to compound asymptotic approximations Presents a novel, well-explained method of meso-scale approximations for bodies with non-periodic multiple perforations Contains illustrations and numerical examples for a range of physically realisable configurations
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2077)
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Table of contents (10 chapters)
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Front Matter
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Green’s Functions in Singularly Perturbed Domains
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Front Matter
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Green’s Functions in Singularly Perturbed Domains
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Green’s Tensors for Vector Elasticity in Bodies with Small Defects
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Front Matter
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Green’s Tensors for Vector Elasticity in Bodies with Small Defects
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Meso-scale Approximations: Asymptotic Treatment of Perforated Domains Without Homogenization
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Front Matter
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Back Matter
About this book
Green’s function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green’s functions and solutions of boundary value problems for meso-scale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions.
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.
Authors and Affiliations
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Department of Mathematics, Linköping University, Linköping, Sweden
Vladimir Maz'ya
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Dept. Mathematical Sciences, University of Liverpool, Liverpool, United Kingdom
Alexander Movchan
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School of Engineering, Liverpool John Moores University, Liverpool, United Kingdom
Michael Nieves
Bibliographic Information
Book Title: Green's Kernels and Meso-Scale Approximations in Perforated Domains
Authors: Vladimir Maz'ya, Alexander Movchan, Michael Nieves
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-00357-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Softcover ISBN: 978-3-319-00356-6Published: 14 June 2013
eBook ISBN: 978-3-319-00357-3Published: 07 June 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVII, 258
Number of Illustrations: 7 b/w illustrations, 10 illustrations in colour
Topics: Partial Differential Equations, Approximations and Expansions
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