Tcheugoué Tébou, Louis Roder 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 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 11, 1175-1179 (1997). 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. Cited in 7 Documents 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 Keywords:multiplier technique; integral inequalities PDFBibTeX XMLCite \textit{L. R. Tcheugoué Tébou}, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 11, 1175--1179 (1997; Zbl 0894.35071) Full Text: DOI