Energy decay for a localized degenerate hyperbolic equation in an exterior domain Original Research Article

We derive decay estimates of local energy for wave equations of two types; with a localized weak dissipation a(x)uta(x)ut and a localized strong dissipation ∇⋅(a(x)∇ut)∇⋅(a(x)∇ut) in an exterior domain. The dissipative coefficient a(x)a(x) is a nonnegative function only on a neighborhood of some part of the boundary, and no geometrical conditions are imposed on the boundary.