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Energy estimates for the wave equation with localized nonlinear damping. (Estimations d’énergie pour l’équation des ondes avec un amortissement non linéaire localisé.) (French. Abridged English version) Zbl 0894.35071

Summary: We prove some decay estimates of the energy of the wave equation in a bounded domain. The damping is nonlinear and is effective only in a neighbourhood of a suitable subset of the boundary. The method of proof is direct and is based on multipliers technique and on some integral inequalities due to Haraux and Komornik.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B45 A priori estimates in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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