Remarks on weak stabilization of semilinear wave equations
Université Pierre et Marie Curie, Analyse Numérique, Tour 55-65
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Revised: 11 November 2000
Revised: 4 May 2001
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 Vancostenoble.
Mathematics Subject Classification: 35B35 / 35L55 / 35L90
Key words: Weak stabilization / semilinear / wave equations.
© EDP Sciences, SMAI, 2001