Global existence for semilinear wave equations in exterior domains
Global existence for semilinear wave equations in exterior domains
复制标题
外域半线性波动方程的全局存在性
DOI：
10.1016/s0362-546x(01)00372-8
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Nakao
中科院分区：
文献类型：
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作者：
M. Nakao
我们考虑线性和半线性波动方程的外问题。首先，我们推导出总能量衰减的线性波动方程的局部耗散，这是有效的无穷远和临界部分的边界。这一结果可用于证明半线性波动方程有限能量或H2解的整体存在性。接下来，通过使用本地的能量衰减：我们显示L p估计的线性方程的耗散有效的边界附近的一部分，并再次将其应用到全球存在的半线性方程。
We consider exterior problems for linear and semilinear wave equations. We first derive total energy decay for the linear wave equation with a localized dissipation which is effective near infinity and critical part of the boundary. This can be applied to the proof of the global existence of finite energy or H 2 solutions for semilinear wave equations. Next, by use of the local energy decay: we show L p estimates for the linear equations with a dissipation effective only near a part of the boundary and apply this again to the global existence of semilinear equations.