Scattering Theory for Hyperbolic Operators, Volume 21

Contraction Semigroups and Power Bounded Operators. The Cauchy Problem for the Wave Equation. Scattering Theory for Symmetric Systems with Dissipative Boundary Conditions. Disappearing Solutions for Symmetric Systems. Wave Equation with Time-Dependent Potential. Inverse Scattering Problem for Time-Dependent Potentials. Wave Equation in the Exterior of a Moving Obstacle. Leading Singularity of the Scattering Kernel. Appendices. References. Index.

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.