Global existence of solutions for 2-D semilinear wave equations with dissipation localized near infinity in an exterior domain

We shall derive some global existence results to semilinear wave equations with a damping coefficient localized near infinity for very special initial data in H1 o×L2. This problem is dealt with in the two-dimensional exterior domain with a star-shaped complement. In our result, a power p on the non-linear term |u|p is strictly larger than the two-dimensional Fujita-exponent