Kernel Determination Problems in Hyperbolic Integro-Differential Equations (Infosys Science Foundation Series)

Durdiev, Durdimurod K./ Totieva, Zhanna D.

Springer Verlag, Singapore（2024/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 368 p.
• 言語 ENG
• 商品コード 9789819922628

Full Description

This book studies the construction methods for solving one-dimensional and multidimensional inverse dynamical problems for hyperbolic equations with memory. The theorems of uniqueness, stability and existence of solutions of these inverse problems are obtained. This book discusses the processes, by using generalized solutions, the spread of elastic or electromagnetic waves arising from sources of the type of pulsed directional "impacts" or "explosions". This book presents new results in the study of local and global solvability of kernel determination problems for a half-space. It describes the problems of reconstructing the coefficients of differential equations and the convolution kernel of hyperbolic integro-differential equations by the method of Dirichlet-to-Neumann. The book will be useful for researchers and students specializing in the field of inverse problems of mathematical physics.

Contents

Chapter 1: Local Solvability of One-dimensional Kernel Determination Problems.- Chapter 2: The Solvability of Multidimensional Inverse Problems of a Memory Kernel Determination.- Chapter 3: Global Solvability of Memory Reconstruction Problems.- Chapter 4: Stability in Inverse Problems for Determining Two Unknowns.- Chapter 5: Two-dimensional Special Kernel Determination Problems.- Chapter 6: Some Inverse Problems of Viscoelasticity System with the Known Kernel.- Chapter 7: Kernel Identification Problems in a Viscoelasticity System.- Chapter 1:Dirichlet-to-Neumann Maps Method in Kernel Determining Problems.