Geodesic
Uniqueness of self-similar very singular solution for non-Newtonian polytropic filtration equations with gradient absorption
Electronic journal of differential equations, Tome 2015 (2015)
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 $q>1$.
Classification : 35K65, 35K92, 35K15
Keywords: polytropic filtration, gradient absorption, uniqueness, self-similar, very singular 
@article{EJDE_2015__2015__a67,
     author = {Ye,  Hailong and Yin,  Jingxue},
     title = {Uniqueness of self-similar very singular solution for {non-Newtonian} polytropic filtration equations with gradient absorption},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1433.35186},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a67/}
}
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VL  - 2015
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%A Yin,  Jingxue
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%J Electronic journal of differential equations
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%F EJDE_2015__2015__a67
Ye,  Hailong; Yin,  Jingxue. Uniqueness of self-similar very singular solution for non-Newtonian polytropic filtration equations with gradient absorption. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a67/