Electron. J. Differential Equations, Vol. 2022 (2022), No. 42, pp. 1-19.

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

Caihong Chang, Zhengce Zhang

Abstract:
This article concerns the blow up behavior for the Henon type parabolic equation with exponential nonlinearity,

where $\sigma\geq 0$ and $B_R=\{x\in\mathbb{R}^N: |x|<R\}$. We consider all cases in which blowup of solutions occurs, i.e. $N\geq 10+4\sigma$. Grow up rates are established by a certain matching of different asymptotic behaviors in the inner region (near the singularity) and the outer region (close to the boundary). For the cases $N>10+4\sigma$ 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.

Submitted May 3, 2021. Published June 28, 2022.
Math Subject Classifications: 35A01, 35B40, 35B44, 35K20.
Key Words: Matched expansion; weighted term; stabilization; grow up rate; degeneracy.
DOI: https://doi.org/10.58997/ejde.2022.42

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Caihong Chang
School of Mathematics and Statistics
Xi'an Jiaotong University
Xi'an, 710049, China
email: caihong666@stu.xjtu.edu.cn
Zhengce Zhang
School of Mathematics and Statistics
Xi'an Jiaotong University
Xi'an, 710049, China
email: zhangzc@mail.xjtu.edu.cn

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