On a Nonlinear, Nonlocal Parabolic Problem with Conservation of Mass, Mean and Variance

DOI10.1080/03605302.2011.563402zbMath1242.35144OpenAlexW1981881397MaRDI QIDQ3094713

Marcus Wunsch, Adrian Tudorascu

Publication date: 25 October 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2011.563402

zbMATH Keywords

Wasserstein metricconstrained optimizationgradient flowoptimal mass transportnonlocal parabolic PDEporous-medium-type functionals

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Existence theories in calculus of variations and optimal control (49J99) Fokker-Planck equations (35Q84)

Related Items (4)

Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation ⋮ On a Kirchhoff diffusion equation with integral condition ⋮ On initial inverse problem for nonlinear couple heat with Kirchhoff type ⋮ Existence of solutions for parabolic equations of Kirchhoff type involving variable exponent

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium
• On the Jordan-Kinderlehrer-Otto variational scheme and constrained optimization in the Wasserstein metric
• On the asymptotic behaviour of some nonlocal 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
• Variational principle for general diffusion problems
• Solution of a model Boltzmann equation via steepest descent in the 2-Wasserstein metric
• Asymptotic complexity in filtration equations
• A central limit theorem for solutions of the porous medium equation
• Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for \(u_t = \Delta\varphi(u)\)
• Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Asymptotic behaviour of some nonlocal diffusion problems
• Non-linear diffusion in a finite mass medium
• The Variational Formulation of the Fokker--Planck Equation
• Optimal Transport
• On singular limits of mean-field equations.
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

This page was built for publication: On a Nonlinear, Nonlocal Parabolic Problem with Conservation of Mass, Mean and Variance