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 $t \to \infty$ uniformly in $x \in {\mathbb R}^2$. In particular, our result implies the decay of the energy when the nonlinearity is dissipative. 
Soichiro Katayama, Daisuke Murotani, and Hideaki Sunagawa
math.AP