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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 → ∞ uniformly in \({x \in \mathbb{R}^2}\). In particular, our result implies the decay of the energy when the nonlinearity is dissipative.

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