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

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 $q>1$.

Keywords

• Polytropic filtration
• gradient absorption
• uniqueness
• self-similar
• very singular