On clogged and fast diffusions in porous media with fractional pressure

2025/01/20 by Antonin Chodron de Courcel, de Courcel, Antonin Chodron · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geotechnical and Geomechanical Engineering #Mathematical Physics (math-ph) #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2501.11645

openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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