Local energy decay for wave equations in exterior domains with regular or fast decaying dissipations

Abstract

Decaying properties of the local energy for the dissipative wave equations with the Dirichlet boundary conditions in exterior domains are discussed. For the dissipation coefficient, natural conditions ensuring that waves trapped by obstacles may lose their energy are considered. Under this setting, the cases that the dissipation coefficient does not have a compact support, but has some regularities are treated. Further, the cases that the dissipation coefficients decay sufficiently fast at infinity are also discussed.