Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions
Blow up for initial boundary value problem of critical semilinear wave equation in two space dimensions
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DOI：
10.3934/cpaa.2018072
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发表时间：
2018-04
影响因子：
1
通讯作者：
Ning-An Lai;Yi Zhou
中科院分区：
文献类型：
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作者：
Ning-An Lai;Yi Zhou
本文研究了具有临界功率的二维空间中半线性波动方程的外区域初边值问题。基于矛盾论证，我们证明了解将在有限时间内爆破。这补充了Smith，Sogge和Wang[20]的超临界情形的存在结果，以及Li和Wang[14]在二维空间中的亚临界情形的结果。
This paper focuses on the initial boundary value problem of semilinear wave equation in exterior domain in two space dimensions with critical power. Based on the contradiction argument, we prove that the solution will blow up in a finite time. This complements the existence result of supercritical case by Smith, Sogge and Wang [ 20 ] and blow up result of subcritical case by Li and Wang [ 14 ] in two space dimensions.