Asymptotic theory of dynamic boundary value problems in irregular domains / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov.
2021
QA379
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Title
Asymptotic theory of dynamic boundary value problems in irregular domains / Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov.
Author
Korikov, Dmitrii.
ISBN
9783030653729 (electronic bk.)
3030653722 (electronic bk.)
9783030653712
3030653714
3030653722 (electronic bk.)
9783030653712
3030653714
Publication Details
Cham : Birkhäuser, 2021.
Language
English
Description
1 online resource (xi, 399 pages)
Item Number
10.1007/978-3-030-65372-9 doi
Call Number
QA379
Dewey Decimal Classification
515/.35
Summary
This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
Bibliography, etc. Note
Includes bibliographical references.
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Access limited to authorized users.
Source of Description
Description based on print version record.
Added Author
Plamenevskiĭ, B. A.
Sarafanov, Oleg.
Sarafanov, Oleg.
Series
Operator theory, advances and applications ; v. 284.
Available in Other Form
Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains.
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Table of Contents
Introduction
Wave equation in domains with edges
Hyperbolic systems in domains with conical points
Elastodynamics in domains with edges
On dynamic Maxwell System in domains with edges
Schroedinger and Germain-Lagrange equations in a domain with corners
Asymptotics of solutions to wave equation in singularity perturbed domains
Asymptotics of solutions to non-stationary Maxwell System in a domain with small cavities.
Wave equation in domains with edges
Hyperbolic systems in domains with conical points
Elastodynamics in domains with edges
On dynamic Maxwell System in domains with edges
Schroedinger and Germain-Lagrange equations in a domain with corners
Asymptotics of solutions to wave equation in singularity perturbed domains
Asymptotics of solutions to non-stationary Maxwell System in a domain with small cavities.