Geodesic
Remarks on weak stabilization of semilinear wave equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 553-560

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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 Vancostenoble.

Classification : 35B35, 35L55, 35L90
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://geodesic.mathdoc.fr/item/COCV_2001__6__553_0/}
}
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Haraux, Alain. Remarks on weak stabilization of semilinear wave equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 553-560. http://geodesic.mathdoc.fr/item/COCV_2001__6__553_0/