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Remarks on weak stabilization of semilinear wave equations

Published online by Cambridge University Press:  15 August 2002

Alain Haraux
Alain Haraux*
Affiliation:
Université Pierre et Marie Curie, Analyse Numérique, Tour 55-65 5 étage, 4 place Jussieu, 75252 Paris Cedex 05, France; [email protected].
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Abstract

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 nonnegligible sub-region for at least one sign of the velocity, all solutions of theperturbed system converge weakly to 0 as time tends to infinity. We present here asimple and natural method of proof of this kind of property, implying as a consequencesome recent very general results of Judith Vancostenoble.

Keywords

Weak stabilizationsemilinearwave equations.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 553 - 560
Copyright
© EDP Sciences, SMAI, 2001

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