Life-span of Blowup Solutions to Semilinear Wave Equation with Space-dependent Critical Damping
Life-span of Blowup Solutions to Semilinear Wave Equation with Space-dependent Critical Damping
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DOI：
10.1619/fesi.64.137
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发表时间：
2017-09
期刊：
影响因子：
--
通讯作者：
M. Ikeda;M. Sobajima
中科院分区：
文献类型：
--
作者：
M. Ikeda;M. Sobajima
本文研究具有临界空间依赖阻尼项(DW:$V$)的半线性波动方程初值问题的爆炸现象。本文的主要结果是给出问题的解决方案，并在 $\frac{N}{N-1}<p\leq p_S(N+V_0)$ 时为该解决方案的寿命提供准确的估计，其中 $p_S(N)$ 是 (DW:$0$) 的施特劳斯指数。证明的主要思想源于Zhou--Han (2014, MR3169791) 提出的(DW:$0$) 测试函数技术。此外，我们为临界和奇异阻尼系数$|x|^{-1}$找到了一个新的阈值$V_0=\frac{(N-1)^2}{N+1}$。
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$V$). The main result of the present paper is to give a solution of the problem and to provide a sharp estimate for lifespan for such a solution when $\frac{N}{N-1}<p\leq p_S(N+V_0)$, where $p_S(N)$ is the Strauss exponent for (DW:$0$). The main idea of the proof is due to the technique of test functions for (DW:$0$) originated by Zhou--Han (2014, MR3169791). Moreover, we find a new threshold value $V_0=\frac{(N-1)^2}{N+1}$ for the coefficient of critical and singular damping $|x|^{-1}$.