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

Resource Information

The work Green's kernels and meso-scale approximations in perforated domains represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

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

Statement of responsibility

Vladimir Maz'ya, Alexander Movchan, Michael Nieves

Creator

• Mazʹi︠a︡, V. G

Contributor

• Movchan, A. B., (Alexander B)
• Nieves, Michael

Subject

• Approximation theory
• Approximation theory
• Approximations and Expansions.
• Boundary value problems
• Boundary value problems
• Boundary value problems
• Boundary value problems -- Asymptotic theory
• Boundary value problems -- Asymptotic theory
• Boundary value problems -- Asymptotic theory
• Differential equations, Elliptic -- Asymptotic theory
• Differential equations, Elliptic -- Asymptotic theory
• Differential equations, Elliptic -- Asymptotic theory
• Differential equations, partial.
• Green's functions
• Green's functions
• Green's functions
• Inhomogeneous materials -- Mathematical models
• Inhomogeneous materials -- Mathematical models
• Inhomogeneous materials -- Mathematical models
• Mathematics.
• Partial Differential Equations.
• Approximation theory

Language

eng

Summary

There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. 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

Member of

• Lecture notes in mathematics (Springer-Verlag), 2077
• Lecture notes in mathematics (Springer-Verlag), 2077.

Cataloging source

GW5XE

Dewey number

515/.22

Illustrations

illustrations

Index

index present

LC call number

QA331

LC item number

.M39 2013

Literary form

non fiction

Nature of contents

• dictionaries
• bibliography

Series statement

Lecture notes in mathematics,

Series volume

2077