Tuomo Kuusi, Léonard Monsaingeon, Juha Videman
Published 2014-12-17Version 1
We investigate systems of degenerate parabolic equations idealizing reactive solute transport in porous media. Taking advantage of the inherent structure of the system that allows to deduce a scalar Generalized Porous Medium Equation for the sum of the solute concentrations, we show existence of a unique weak solution to the coupled system and derive regularity estimates. We also prove that the system supports solutions propagating with finite speed thus giving rise to free boundaries and interaction of compactly supported initial concentrations of different species.
On a system of partial differential equations of Monge-Kantorovich type
A generalized porous medium equation related to some singular quasilinear problems
The generalized porous medium equation on graphs: existence and uniqueness of solutions with $\ell^1$ data
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