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Zbl 0988.35029
Haraux, Alain
Remarks on weak stabilization of semilinear wave equations. (English)
[J] ESAIM, Control Optim. Calc. Var. 6, 553-560 (2001). ISSN 1292-8119; ISSN 1262-3377/e

Summary: If a second-order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly nonmonotone damping term, which is effective in a nonnegligible subregion for at least one sign of the velocity, all solutions of the perturbed system converge weakly to zero 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.

MSC 2000:: *35B40 Asymptotic behavior of solutions of PDE
35L90 Abstract hyperbolic evolution equations
35B35 Stability of solutions of PDE
35L55 Higher order hyperbolic systems
35L70 Second order nonlinear hyperbolic equations

Keywords: semilinear conservative equation; essentially oscillatory solutions; nonmonotone damping term

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