arXiv:2501.11645 Abstract | arXiv Analytics

arXiv:2501.11645 [math.AP]Abstract References Reviews Resources

On clogged and fast diffusions in porous media with fractional pressure

Published 2025-01-20Version 1

We study the existence and infinite-speed propagation of solutions to models arising in porous media, when the mobility is highly degenerate (inverse power law). The approach is based on maximum principles for the fractional Laplacian, and allows to derive lower bounds on solutions in a straightforward manner. Finally, in the case of clogged porous media, where the mobility vanishes at points of unbounded density, solutions that become instantaneously bounded are constructed.

Categories: math.AP, math-ph, math.MP

Keywords: porous media, fractional pressure, fast diffusions, inverse power law, derive lower bounds

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