Global existence of weak solutions for two-dimensional semilinear wave equations with strong damping in an exterior domain

We consider two-dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power-type nonlinearity |u|p|u|p. If the initial data have a small weighted energy, we shall derive a global existence and energy decay results in the case when the power pp of the nonlinear term satisfies p>6p>6.