Scattering Theory for Hyperbolic Operators

✍ Scribed by Vesselin Petkov (Eds.)

• Publisher: Elsevier Science Ltd
• Year: 1989
• Tongue: English
• Leaves: 391
• Series: Studies in Mathematics and Its Applications 21
• Category: Library

✦ Synopsis

Scattering Theory for dissipative and time-dependent systems has been intensively studied in the last fifteen years. The results in this field, based on various tools and techniques, may be found in many published papers. This monograph presents an approach which can be applied to spaces of both even and odd dimension. The ideas on which the approach is based are connected with the RAGE type theorem, with Enss' decomposition of the phase space and with a time-dependent proof of the existence of the operator W which exploits the decay of the local energy of the perturbed and free systems. Some inverse scattering problems for time-dependent potentials, and moving obstacles with an arbitrary geometry, are also treated in the book.

✦ Table of Contents

Content:
Editors
Page ii

Edited by
Page iii

Copyright page
Page iv

Introduction
Pages ix-xiv

Chapter I Contraction Semigroups and Power Bounded Operators
Pages 1-21

Chapter II The Cauchy Problem for the Wave Equation
Pages 23-67

Chapter III Scattering Theory for Symmetric Systems with Dissipative Boundary Conditions
Pages 69-118

Chapter IV Disappearing Solutions for Symmetric Systems
Pages 119-155

Chapter V Wave Equation with Time-Dependent Potential
Pages 157-223

Chapter VI Inverse Scattering Problem for Time-Dependent Potentials
Pages 225-246

Chapter VII Wave Equation in the Exterior of a Moving Obstacle
Pages 247-294

Chapter VIII Leading Singularity of the Scattering Kernel
Pages 295-343

Appendix I
Pages 345-348

Appendix II
Pages 349-353

Refereces
Pages 355-370

Index
Pages 371-373

Erratum
Page 375