Global existence and blow-up of solutions for the heat equation with exponential nonlinearity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Fujishima, Yohei¹ 

[1] Shizuoka Univ, Fac Engn, Dept Math & Syst Engn, 3-5-1 Johoku, Hamamatsu, Shizuoka 4328561, Japan

关键词: Nonlinear heat equation;    Exponential nonlinearity;    Blow-up;    Global in time existence;    Forward self-similar solution;   

DOI  :  10.1016/j.jde.2018.01.048

来源: Elsevier

【 摘 要 】

We are concerned with the existence of global in time solution for a semilinear heat equation with exponential nonlinearity { partial derivative(t)u = Delta u + e(u), x is an element of R-N, t < 0, u(x, 0) = u(0)(x), x is an element of R-N, (P) where up is a continuous initial function. In this paper, we consider the case where up decays to -infinity at space infinity, and study the optimal decay bound classifying the existence of global in time solutions and blowing up solutions for (I)). In particular, we point out that the optimal decay bound for up is related to the decay rate of forward self-similar solutions of at partial derivative(t)u = Delta u + e(u). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free