Tauberian Theory of Wave Fronts in Linear Hereditary Elasticity, 1st ed. 2020

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.

Constructs a rigorous mathematical approach to linear hereditary problems of wave propagation theory

Opens unforeseen applications to fractal environments

Presents a classification of near-front asymptotics of solutions to considered equations