Rate of Type II blowup for a semilinear heat equation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

按检索

Rate of Type II blowup for a semilinear heat equation

Authors:

Noriko Mizoguchi

Institution:

(1) Department of Mathematics, Tokyo Gakugei University, Koganei, Tokyo 184-8501, Japan

Abstract:

A solution u of a Cauchy problem for a semilinear heat equation

$\left\{ \begin{array}{ll}u_{t} = \Delta u + u^{p} & \quad {\rm in}\, {\bf R}^N \times (0,\,T),\\u(x,0) = u_{0}(x) \geq 0 & \quad {\rm in}\, {\bf R}^N \end{array} \right.$

is said to undergo Type II blowup at t = T if lim sup $_{t \nearrow T} (T-t)^{1/(p-1)} |u(t)|_\infty = \infty .$ Let $\varphi_\infty$ be the radially symmetric singular steady state. Suppose that $u_0 \in L^\infty$ is a radially symmetric function such that $u_0 - \varphi_\infty$ and (u ₀)_t change sign at most finitely many times. We determine the exact blowup rate of Type II blowup solution with initial data u ₀ in the case of p > p _L, where p _L is the Lepin exponent.

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35K20 35K55 58K57

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏