Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains Operator Theory Advances and Applications 284 1st Edition by Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov ISBN 3030653714 9783030653712

Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains Operator Theory Advances and Applications 284 1st Edition by Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov – Ebook PDF Instant Download/Delivery: 3030653714, 9783030653712
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ISBN 10: 3030653714 
ISBN 13: 9783030653712
Author: Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov

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.

Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains Operator Theory Advances and Applications 284 1st Table of contents:

1. Introduction
2. Wave Equation in Domains with Edges
3. Hyperbolic Systems in Domains with Conical Points
4. Elastodynamics in Domains with Edges
5. On Dynamic Maxwell System in Domains with Edges
6. Schroedinger and Germain-Lagrange Equations in a Domain with Corners
7. Asymptotics of Solutions to Wave Equation in Singularly Perturbed Domains
8. Asymptotics of Solutions to Non-stationary Maxwell System in a Domain with Small Cavities

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Tags: Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov, Asymptotic, Theory