Glasnik Matematicki, Vol. 43, No.2 (2008), 375-386.

ENERGY DECAY ESTIMATES FOR A WAVE EQUATION WITH NONLINEAR BOUNDARY FEEDBACK

Mohammad Cherkaoui and Naji Yebari

Université Abdelmalek Essaadi, Département de Mathematiques, Faculté des Sciences, B. P. 2121, Tetouan, Maroc
e-mail: nyebari@hotmail.com

Abstract.   We study a wave equation in one dimensional space with nonlinear dissipative boundary feedback at both ends. We prove existence and uniqueness of solution, strong and uniform exponential decay of energy under some conditions in the nonlinear feedback. Decay rate estimates of the energy are given under weak growth assumptions on the feedback functions.

2000 Mathematics Subject Classification.   35L05, 35L20, 93D15, 34D20.

Key words and phrases.   Wave equation, nonlinear boundary value problems, stabilization of systems by feedback, Lyapunov stability, polynomial decay.

DOI: 10.3336/gm.43.2.10

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