Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains

This book explores dynamic boundary value problems in irregular domains, focusing on singularities and their implications for elastodynamics and electrodynamics.

This book delves into the intricacies of dynamic boundary value problems encountered in domains characterized by singularities of two distinct types. The first type involves boundaries with 'edges' of varying dimensions, including polygons, cones, lenses, and polyhedra. These singularities represent a foundational aspect of the study, highlighting the unique challenges they pose in mathematical modeling. The second type focuses on 'singularly perturbed edges,' which include smoothed corners, edges, and small holes. The interplay between these singularities and the behavior of solutions is a central theme in the exploration of these dynamic problems.

In the context of an 'irregular' domain featuring such singularities, the book addresses a range of dynamic issues, including elastodynamics and electrodynamics. It aims to provide a thorough understanding of the asymptotic behavior of solutions as they approach the boundaries defined by these singularities. This analysis is crucial for both theoretical insights and practical applications, as it sheds light on how solutions evolve in the presence of complex geometries.

Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains presents a comprehensive collection of results and methodologies that have significant implications in mathematical physics and engineering. It is particularly valuable for specialists in mathematical physics, partial differential equations, and asymptotic methods, offering a rich resource for advancing knowledge in these fields.