具有指数非线性的Henon型抛物型方程爆破解的渐近性质

Pub Date : 2023-07-09 DOI:10.58997/ejde.2022.42

Caihong Chang, Zhengce Zhang

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引用次数: 0

摘要

本文讨论了具有指数非线性的Henon型抛物方程$$ u_t=\Delta u+|x|^{\sigma}e^u\quad \text{in } B_R\times \mathbb{R}_+, $$的爆破行为，其中$\sigma\geq 0$和$B_R=\{x\in\mathbb{R}^N: |x|10+4\sigma$、$N=10+4\sigma$的平稳解的渐近展开形式不同，因此分别讨论了两种情况。此外，还得到了两种情况下不同的内区域宽度。

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Asymptotic behavior of blowup solutions for Henon type parabolic equations with exponential nonlinearity

This article concerns the blow up behavior for the Henon type parabolic equation withexponential nonlinearity, $$ u_t=\Delta u+|x|^{\sigma}e^u\quad \text{in } B_R\times \mathbb{R}_+, $$ where $\sigma\geq 0$ and $B_R=\{x\in\mathbb{R}^N: |x|10+4\sigma$ and $N=10+4\sigma$, the asymptotic expansions of stationary solutions have different forms, so two cases are discussed separately. Moreover, different inner region widths in two cases are also obtained.

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