Electron. J. Differential Equations, Vol. 2017 (2017), No. 10, pp. 1-10.

Critical exponent for the asymptotic behavior of rescaled solutions to the porous medium equation

Liangwei Wang, Jingxue Yin

Abstract:
In this article, we find that $\mu_c\equiv 2N/(N(m-1)+2)$ is the critical exponent for the asymptotic behavior of rescaled solutions $t^{\mu/2}u(t^\beta x,t)$ for the porous medium equation.

Submitted November 17, 2016. Published January 10, 2017.
Math Subject Classifications: 35B40, 35K65.
Key Words: Complexity; asymptotic behavior; porous medium equation.

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Liangwei Wang
Key Laboratory for Nonlinear Science and System Structure
College of Mathematics and Statistics
Chongqing Three Gorges University
Chongqing 404000, China
email: wanglw08@163.com
Jingxue Yin
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: yjx@scnu.edu.cn

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