The energy decay and asymptotics for a class of semilinear wave equations in two space dimensions

We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions and give an asymptotic description of the solution as t -> infinity uniformly in x is an element of R-2. In particular, our result implies the decay of the energy when the nonlinearity is dissipative.