NONLINEAR WAVE EQUATIONS WITH ACOUSTIC BOUNDARY CONDITIONS

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.