Abstract

In this paper the long time asymptotic behavior of solutions of semilinear symmetric hyperbolic system including Maxwell s equations and the scalar wave equation in an ar bitraty domain are investigated The possibly nonlinear damping term may vanish on a certain subset of the domain It is shown that the solution decays weakly to zero if and only if the initial state is orthogonal to all stationary states In the case that the nonlinear damping is in addition montone also strong local L convergence is shown AMS B Q L L A Introduction The subject of this paper the long time asymptotic behavior of solutions of semilinear hyperbolic systems of the form

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