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Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains: Operator Theory: Advances and Applications, cartea 284

Autor Dmitrii Korikov, Boris Plamenevskii, Oleg Sarafanov
en Limba Engleză Hardback – 2 apr 2021
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.
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Specificații

ISBN-13: 9783030653712
ISBN-10: 3030653714
Pagini: 399
Ilustrații: XI, 399 p. 1 illus. in color.
Dimensiuni: 155 x 235 mm
Greutate: 0.75 kg
Ediția:1st ed. 2021
Editura: Springer International Publishing
Colecția Birkhäuser
Seriile Operator Theory: Advances and Applications, Advances in Partial Differential Equations

Locul publicării:Cham, Switzerland

Cuprins

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.

Textul de pe ultima copertă

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.


Caracteristici

Collects main results from scattered papers in this monograph Presents a wide range of applications Extends previously published works with new insights