### NONLINEAR WAVE EQUATIONS WITH ACOUSTIC BOUNDARY CONDITIONS

#### 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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