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.
Table of Content
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.
About the author
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.
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