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

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

2011-11-17

arxiv.org/abs/1111.4231v1

Mathematics

Analysis of PDEs

24 pages

Scientific paper

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.

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