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.
Author(s): Vesselin Petkov (Eds.)
Series: Studies in Mathematics and Its Applications 21
Publisher: Elsevier Science Ltd
Year: 1989
Language: English
Pages: 1-375
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
