Tauberian Theory of Wave Fronts in Linear Hereditary Elasticity

Alexander A. Lokshin

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English

Springer Verlag, Singapore
23 October 2021

Functional analysis & transforms; Integral calculus & equations; Mathematical physics; Mechanical engineering

The objective of this book is to construct a rigorous mathematical approach to linear hereditary problems of wave propagation theory and demonstrate the efficiency of mathematical theorems in hereditary mechanics. By using both real end complex Tauberian techniques for the Laplace transform, a classification of near-front asymptotics of solutions to considered equations is given—depending on the singularity character of the memory function. The book goes on to derive the description of the behavior of these solutions and demonstrates the importance of nonlinear Laplace transform in linear hereditary elasticity. This book is of undeniable value to researchers working in areas of mathematical physics and related fields.

By: Alexander A. Lokshin
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 1st ed. 2020
Dimensions: Height: 235mm, Width: 155mm,
Weight: 238g
ISBN: 9789811585807
ISBN 10: 9811585806
Pages: 136
Publication Date: 23 October 2021
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Chapter 1. The Problem of Hyperbolicity in Linear Hereditary Elasticity.- Chapter 2. General Hyperbolic Operators with Memory.- Chapter 3. The Wave Equation with Memory.- Appendix: Near Source Behaviour of Fundamental Solutions for Wave Operators with Memory.- References.

ALEXANDER A. LOKSHIN is Professor of Mathematics at the Faculty of Primary Education, Moscow Pedagogical University, Russia, since 1999. He completed his graduation in differential equations in 1973 from the Faculty of Mechanics and Mathematics, Moscow State University, Russia. Professor Lokshin defended his thesis on ""On lacunas and weak lacunas of hyperbolic and quasi-hyperbolic equations"" in 1976 at Moscow State University, Russia. Later, he defended his doctoral dissertation on ""Waves in hereditarily elastic media"" at the Institute of Problems of Mechanics, USSR Academy of Sciences, Russia, in 1985. He served as a junior research fellow at the Moscow Institute of Electronic Engineering and had also worked as a scientific editor for the Moscow University Press, Russia. Coauthor of The Mathematical Theory of Wave Propagation in Media with Memory and Nonlinear Waves in Inhomogeneous and Hereditary Media, Prof. Lokshin has also published several books proposing a visual and at the same time mathematically rigorous justification of the four arithmetic algorithms.