Explicit Barenblatt profiles for fractional porous medium equations

DOI10.1112/blms/bdu045zbMath1297.35273arXiv1312.0469OpenAlexW3102224879MaRDI QIDQ5495356

Yanghong Huang

Publication date: 4 August 2014

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.0469

zbMATH Keywords

self-similar solutionshypergeometric functionsfractional Laplace operatorfractional porous medium equationBarenblatt profile

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Flows in porous media; filtration; seepage (76S05) Classical hypergeometric functions, ({}_2F_1) (33C05) Fractional partial differential equations (35R11) Self-similar solutions to PDEs (35C06)

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Cites Work

• Hitchhiker's guide to the fractional Sobolev spaces
• Barenblatt profiles for a nonlocal porous medium equation
• A fractional porous medium equation
• Nonlinear porous medium flow with fractional potential pressure
• Symmetry and integration methods for differential equations
• Self-similar solutions of a fast diffusion equation that do not conserve mass
• The nonlocal porous medium equation: Barenblatt profiles and other weak solutions
• Finite and infinite speed of propagation for porous medium equations with fractional pressure
• Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
• Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type
• Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
• A General Fractional Porous Medium Equation
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