SELF-SIMILAR SINGULAR SOLUTION OF A P-LAPLACIAN EVOLUTION EQUATION WITH GRADIENT ABSORPTION TERM

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: p-Laplacian evolution equation gradient absorption self-similar singular solution very singular solution.
• 年，卷（期）: 2004,（4）
• 页码范围: 369-383
• 页数: 15页
• 分类号: O175.26.
• 语种: 英文

摘要

In this paper we deal with the self-similar singular solution of the p-Laplacian evolution equation ut = div(|△u|p-2△u) - |△u|q for p ＞ 2 and q ＞ 1 in Rn × (0,∞). We prove that when p ＞ q + n/(n + 1) there exist self-similar singular solutions, while p (≤) q+n/(n+ 1) there is no any self-similar singular solution. In case of existence, the self-similar singular solutions are the self-similar very singular solutions,which have compact support. Moreover, the interface relation is obtained.