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Displaying similar documents to “Asymptotics for some nonlinear damped wave equation : finite time convergence versus exponential decay results”

Remarks on weak stabilization of semilinear wave equations

Alain Haraux (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith...