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.
Keywords: weak stabilization, semilinear, wave equations
@article{COCV_2001__6__553_0, author = {Haraux, Alain}, title = {Remarks on weak stabilization of semilinear wave equations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {553--560}, publisher = {EDP-Sciences}, volume = {6}, year = {2001}, mrnumber = {1849416}, zbl = {0988.35029}, language = {en}, url = {http://www.numdam.org/item/COCV_2001__6__553_0/} }
Haraux, Alain. Remarks on weak stabilization of semilinear wave equations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 6 (2001), pp. 553-560. http://www.numdam.org/item/COCV_2001__6__553_0/
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