Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms

In this paper we develop an intrinsic approach to derivation of energy decay rates for the semilinear wave equation with localized interior nonlinear   monotone damping g(_ut)$g(u_t)$ and a source term  f(u)$f(u)$. The proposed approach allows to consider, in an unified way, much more general classes of hyperbolic problems than addressed before in the literature. These generalizations refer to both geometric and topological aspects of the problem.