Semilinear parabolic equation on bounded domain with critical Sobolev exponent
Semilinear parabolic equation on bounded domain with critical Sobolev exponent
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DOI：
10.1512/iumj.2008.57.3269
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发表时间：
2008
影响因子：
1.1
通讯作者：
Takashi Suzuki
中科院分区：
文献类型：
--
作者：
Takashi Suzuki
本文关注的是半线性抛物线方程 μ t - Δμ = |Μ| R n 中的有界域上的 P-1 μ 具有临界 Sobolev 指数 p = (n+2)/(n-2)。我们研究正解并对它们的全局及时行为进行分类。特别是，当 Ω 是凸且对称时，会显示无限时间内的爆炸。
This paper is concerned with the semilinear parabolic equation μ t - Δμ = |Μ| P-1 μ on bounded domain in R n with the critical Sobolev exponent p = (n+2)/(n-2). We study positive solutions and classify their global in time behavior. Particularly, the blowup in infinite time is shown when Ω is convex and symmetric.