Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains

This book discusses dynamic boundary value problems in domains with singularities of two types: edges of various dimensions and singularly perturbed edges. It describes the asymptotics of solutions near these singularities and has applications in mathematical physics and engineering.

Format: Paperback / softback
Length: 399 pages
Publication date: 02 April 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the realm of dynamic boundary value problems, focusing on domains with singularities of two distinct types. The first type encompasses edges of varying dimensions on the boundary, including polygons, cones, lenses, polyhedra, and more. These domains are characterized by their intricate geometries. On the other hand, the second type consists of singularly perturbed edges, such as smoothed corners, edges, and small holes. These singularities introduce an additional level of complexity to the problem.

A remarkable feature of these domains is that their behavior is influenced by a small parameter, which determines the transition from the limit domain to the perturbed one. As the parameter approaches zero, the boundary of the limit domain undergoes a smooth transformation, while the boundary of the perturbed domain exhibits singularities of the first type. This intricate interplay between the boundaries leads to fascinating phenomena such as the smoothing of conical points and the formation of small cavities near edges.

Within these domains, problems of elastodynamics, electromagnetism, and other dynamic problems are explored. The primary objective is to describe the asymptotic behavior of solutions near the singularities of the boundary. The presented results and methodologies have broad applications in mathematical physics and engineering, spanning various fields. This book is specifically designed for experts in mathematical physics, partial differential equations, and asymptotic methods, offering a deep understanding of the complexities involved in dynamic boundary value problems with singularities.

Weight: 629g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030653743
Edition number: 1st ed. 2021