Global existence and blow-up of solutions for the heat equation with exponential nonlinearity
Global existence and blow-up of solutions for the heat equation with exponential nonlinearity
复制标题
指数非线性热方程解的全局存在性和爆炸
DOI：
10.1016/j.jde.2018.01.048
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发表时间：
2018
影响因子：
2.4
通讯作者：
Fujishima Yohei
中科院分区：
文献类型：
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作者：
Scipio Cuccagna and Masaya Maeda;Yohei Fujishima and Norisuke Ioku;Fujishima Yohei
研究了一类具有指数非线性项的半线性热方程（P）{tu = Δ u+ eu，x∈ RN，t> 0，u（x，0）= u 0（x），x∈ RN，其中u 0是连续的初始函数.在本文中，我们考虑的情况下，u 0衰减到−∞在空间无穷远，并研究的最佳衰减界分类的存在性的整体在时间上的解决方案和爆破解决方案（P）。特别地，我们指出u 0的最佳衰减界与方程u= Δ u+ eu的前向自相似解的衰减率有关.
We are concerned with the existence of global in time solution for a semilinear heat equation with exponential nonlinearity (P){∂ t u= Δ u+ e u, x∈ R N, t> 0, u (x, 0)= u 0 (x), x∈ R N, where u 0 is a continuous initial function. In this paper, we consider the case where u 0 decays to−∞ at space infinity, and study the optimal decay bound classifying the existence of global in time solutions and blowing up solutions for (P). In particular, we point out that the optimal decay bound for u 0 is related to the decay rate of forward self-similar solutions of∂ t u= Δ u+ e u.