Abstract
In this article we consider the initial-boundary value problem for linear and nonlinear wave equations in an exterior domain Ω in RN with the homogeneous Dirichlet boundary condition. Under the effect of localized dissipation like a(x)ut we derive both of local and total energy decay estimates for the linear wave equation and apply these to the existence problem of global solutions of semilinear and quasilinear wave equations. We make no geometric condition on the shape of the boundary ∂Ω.
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