Almost global existence for nonlinear wave equations in an exterior   domain in two space dimensions
  In this paper we deal with the exterior problem for a system of nonlinear wave equations in two space dimensions, assuming that the initial data is small and smooth. We establish the same type of lower bound of the lifespan for the problem as that for the Cauchy problem, despite of the weak decay property of the solution in two space dimensions. 
Hideo Kubo
math-ph math.MP