Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure

DOI10.1016/j.jde.2014.10.003zbMath1307.35311arXiv1407.4392OpenAlexW1975080668MaRDI QIDQ473063

J. Herrera, Sumit K. Garg

Publication date: 21 November 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4392

zbMATH Keywords

asymptotic behaviourporous medium equationfunctional inequalitiesentropy dissipationfractional operators

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Fractional derivatives and integrals (26A33) Degenerate parabolic equations (35K65) Fractional partial differential equations (35R11)

Related Items (17)

The fractional Fisher information and the central limit theorem for stable laws ⋮ The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation ⋮ Optimal functional inequalities for fractional operators on the sphere and applications ⋮ 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 ⋮ Some free boundary problems involving non-local diffusion and aggregation ⋮ Long-time asymptotics for a 1D nonlocal porous medium equation with absorption or convection ⋮ Multipole expansion of the fundamental solution of a fractional degree of the Laplace operator ⋮ Global solutions of aggregation equations and other flows with random diffusion ⋮ A gradient flow approach to the porous medium equation with fractional pressure ⋮ The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion ⋮ Complexity of asymptotic behavior of solutions for the fractional porous medium equation ⋮ Existence of weak solutions for a general porous medium equation with nonlocal pressure ⋮ Entropy inequalities for stable densities and strengthened central limit theorems ⋮ Asymptotic behaviour for the fractional heat equation in the Euclidean space ⋮ Classical solutions for fractional porous medium flow ⋮ Analysis and mean-field derivation of a porous-medium equation with fractional diffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity of solutions of the fractional porous medium flow
• Dimensionality of local minimizers of the interaction energy
• A mass-transportation approach to a one dimensional fluid mechanics model with nonlocal velocity
• Hitchhiker's guide to the fractional Sobolev spaces
• First-order global asymptotics for confined particles with singular pair repulsion
• Barenblatt profiles for a nonlocal porous medium equation
• Nonlinear porous medium flow with fractional potential pressure
• Contractions in the 2-Wasserstein length space and thermalization of granular media
• Asymptotics of the fast diffusion equation via entropy estimates
• A non-local model for a swarm
• A convexity principle for interacting gases
• Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• Long-time asymptotics of kinetic models of granular flows
• Mass transportation proofs of free functional inequalities, and free Poincaré inequalities
• Asymptotic behaviour of a porous medium equation with fractional diffusion
• One-dimensional kinetic models of granular flows
• Vorticity and Incompressible Flow
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• A Primer of Swarm Equilibria
• Blow-up in multidimensional aggregation equations with mildly singular interaction kernels
• Logarithmic Sobolev Inequalities
• Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations
• A kinetic equation for granular media
• Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

This page was built for publication: Exponential convergence towards stationary states for the 1D porous medium equation with fractional pressure