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
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DOI：
10.1007/s00028-012-0160-4
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发表时间：
2012-07
影响因子：
1.4
通讯作者：
S. Katayama;Daisuke Murotani;Hideaki Sunagawa
中科院分区：
文献类型：
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作者：
S. Katayama;Daisuke Murotani;Hideaki Sunagawa
考虑二维空间中具有小初值的半线性波动方程。对一类具有三次非线性项的波动方程，证明了小振幅解的整体存在性，并给出了在中的解ast→ ∞的一致渐近描述.特别是，我们的结果意味着当非线性耗散时能量的衰减。
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 ast→ ∞ uniformly in. In particular, our result implies the decay of the energy when the nonlinearity is dissipative.