Decay of solutions of the wave equation in a star-shaped domain with nonlinear boundary feedback

1993/11/01 by Francis Conrad, Françis Conrad, Bopeng Rao · 4 citations
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems

paper · pdf · doi:10.3233/asy-1993-7301

Abstract

We study the uniform stabilization of the wave equation by means of a nonlinear dissipative boundary feedback. We consider a Neumann condition on the whole boundary, and the observation is the boundary displacement and velocity. We obtain, in a nonlinear framework, estimates of the decay, for any displacement. We establish a similar result for the one-dimensional wave equation with a variable coefficient.

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