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NONLINEAR WAVE EQUATIONS WITH ACOUSTIC BOUNDARY CONDITIONS

Gladson O. Antunes, C.L. Frota, M.D.G. Da Silva, L.A. Medeiros

Abstract


In this paper we investigate the existence and uniqueness of solution of a initial boundary value problem for a nonlinear wave operator with weak internal damping of the type

\[

L\left(  u\right)  =\frac{\partial^{2}u}{\partial t^{2}}-\Delta u+\left\vertu\right\vert ^{\rho}+\beta\frac{\partial u}{\partial t}\text{, }\rho>1,\text{}\beta>0\text{,}

\]

with acoustic boundary conditions.


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