Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains / by Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov.

Format:

Book

Author/Creator:

Korikov, Dmitrii, author.

Plamenevskiĭ, B. A., author.

Sarafanov, Oleg, author.

Series:

Advances in Partial Differential Equations, 2504-3595 ; 284

Language:

English

Subjects (All):

Mathematical analysis.

Approximation theory.

Analysis.

Approximations and Expansions.

Local Subjects:

Analysis.

Approximations and Expansions.

Physical Description:

1 online resource (xi, 399 pages)

Edition:

1st ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2021.

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.

Contents:

Elliptic boundary value problems in domains with piecewise smooth boundary

Wave equation in domains with conical points

Hyperbolic systems in domains with edges

Non-stationary Maxwell system in domains with conical points

Elastodynamics problems in domains with edges

Wave equation in singularly perturbed domains

Non-stationary Maxwell system in domains with small holes

Jermain–Lagrange dynamic plate equation in a domain with corner points.

Notes:

Includes bibliographical references and index.

ISBN:

3-030-65372-2

OCLC:

1246578700