具有指数非线性的Henon型抛物型方程爆破解的渐近性质

IF 0.8 4区数学 Q2 MATHEMATICS

Electronic Journal of Differential Equations 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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来源期刊

Electronic Journal of Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

3 months

期刊介绍： All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.