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.
Inhoudsopgave
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.
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