Local Decay of Solutions for Symmetric Hyperbolic Systems with Dissipative and Coercive Boundary Conditions in Exterior Domains

Abstract

P. D. Lax and R. S. Phillips approached the scattering theory for wave equation or symmetric hyperbolic systems with conservative and coercive boundary conditions by time-depended methods in their book Scattering Theory. We have seen whether the methods in this book are applicable to other cases or not. If the interest is restricted to local decay, they are applicable to solutions for symmetric hyperbolic systems with dissipative and coercive boundary conditions when the dimension of space-like > 3. We report this here. We consider the following mixed problem in Ox[0, °o)