Global existence for semilinear wave equations exterior to nontrapping   obstacles
  In this paper, we show global existence, in spatial dimensions greater than or equal to four, for semilinear wave equations with quadratic nonlinearities exterior to a nontrapping obstacle. This extends the previous work of Shibata-Tsutsumi and Hayashi. Shibata-Tsutsumi showed the result for spatial dimensions greater than or equal to 6, and Hayashi proved the result exterior to a ball. 
Jason Metcalfe