Electron. J. Diff. Equ., Vol. 2015 (2015), No. 83, pp. 1-9.

Uniqueness of self-similar very singular solution for non-Newtonian polytropic filtration equations with gradient absorption

Hailong Ye, Jingxue Yin

Abstract:
Uniqueness of self-similar very singular solutions with compact support are proved for the non-Newtonian polytropic filtration equation with gradient absorption
$$ \frac{\partial u}{\partial t} =\hbox{div}(|\nabla u^m|^{p-2}\nabla u^m) -|\nabla u|^{q},\quad x\in \mathbb{R}^N,\quad t>0, $$
where $m>0$, $p>1$, $m(p-1)>1$ and $q>1$.

Submitted November 20, 2014. Published April 7, 2015.
Math Subject Classifications: 35K65, 35K92, 35K15.
Key Words: Polytropic filtration; gradient absorption; uniqueness; self-similar; very singular.

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Hailong Ye
School of Mathematical Sciences
South China Normal University
Guangzhou, Guangdong 510631, China
email: ye2006hailong@yeah.net
Jingxue Yin
School of Mathematical Sciences
South China Normal University
Guangzhou, Guangdong 510631, China
email: yjx@scnu.edu.cn

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