Two dimensional exterior mixed problem for semilinear damped wave equations

We consider two dimensional exterior mixed problems for a semilinear damped wave equation with a power type nonlinearity p|u|. For compactly supported initial data, which have a small energy we shall derive global in time existence results in the case when the power of the nonlinearity satisfies 2<p<+∞. This generalizes a previous result of [J. Differential Equations 200 (2004) 53-68], which dealt with a radially symmetric solution.