Infinite-dimensional porous media equations and optimal transportation

DOI10.1007/s00028-009-0047-1zbMath1239.35064OpenAlexW2094545919MaRDI QIDQ423402

Luigi Ambrosio, Edoardo Mainini

Publication date: 2 June 2012

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

Full work available at URL: https://doi.org/10.1007/s00028-009-0047-1

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Reaction-diffusion equations (35K57) Variational problems in a geometric measure-theoretic setting (49Q20) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

Nonlinear Fokker-Planck-Kolmogorov equations in Hilbert spaces ⋮ Multi-component multiphase porous flow

Cites Work

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• Existence and stability for Fokker-Planck equations with log-concave reference measure
• Stability of a 4th-order curvature condition arising in optimal transport theory
• Entropy solutions for nonlinear degenerate problems
• A convexity principle for interacting gases
• Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
• Constrained steepest descent in the 2-Wasserstein metric
• Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric
• An introduction to infinite-dimensional analysis
• Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Strong convergence results related to strict convexity
• The Variational Formulation of the Fokker--Planck Equation
• Dynamical systems in the variational formulation of the Fokker-Planck equation by the Wasserstein metric