Finite speed of propagation for a non-local porous medium equation

DOI10.4064/cm6511-12-2015zbMath1337.35118arXiv1411.4752OpenAlexW2964015769MaRDI QIDQ2804259

Cyril Imbert

Publication date: 28 April 2016

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4752

zbMATH Keywords

finite speed of propagationfractional Laplaciannon-local porous medium equationnon-local non-linear pressure law

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (7)

Lie symmetry analysis, conservation laws and separation variable type solutions of the time-fractional porous medium equation ⋮ Finite and infinite speed of propagation for porous medium equations with nonlocal pressure ⋮ A gradient flow approach to the porous medium equation with fractional pressure ⋮ Complexity of asymptotic behavior of solutions for the fractional porous medium equation ⋮ Regularity of solutions of a fractional porous medium equation ⋮ Existence of weak solutions for a general porous medium equation with nonlocal pressure ⋮ Apriori estimates for fractional diffusion equation

Cites Work

• Barenblatt profiles for a nonlocal porous medium equation
• Nonlinear porous medium flow with fractional potential pressure
• The nonlocal porous medium equation: Barenblatt profiles and other weak solutions
• Finite and infinite speed of propagation for porous medium equations with fractional pressure

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