具有空间相关临界阻尼的半线性波动方程爆破解的寿命

Pub Date : 2017-09-13 DOI:10.1619/fesi.64.137

M. Ikeda, M. Sobajima

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引用次数: 10

摘要

本文研究了具有临界空间相关阻尼项（DW:$V$）的双线性波动方程初值问题的爆破现象。当$\frac｛N｝｛N-1｝＜p\leq p_S（N+V_0）$时，本文的主要结果是给出了该问题的解决方案，并对这种解决方案的寿命进行了尖锐的估计，其中$p_S（N）$是（DW:$0$）的Strauss指数。证明的主要思想是由于周-韩（2014，MR3169791）提出的（DW:0$）的测试函数技术。此外，我们还发现了临界和奇异阻尼系数$|x|^{-1}$的一个新的阈值$V_0=\frac{（N-1）^2}{N+1}$。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Life-span of Blowup Solutions to Semilinear Wave Equation with Space-dependent Critical Damping

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}

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