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

Abstract

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.

24 pages

References in corpus (1)

• Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions