Entropy dissipation semi-discretization schemes for Fokker-Planck equations

DOI10.1007/s10884-018-9659-xzbMath1416.65212arXiv1608.02628OpenAlexW2963985578MaRDI QIDQ2419932

Wuchen Li, Shui-Nee Chow, Luca Dieci, Hao-Min Zhou

Publication date: 4 June 2019

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

Full work available at URL: https://arxiv.org/abs/1608.02628

zbMATH Keywords

Fokker-Planck equationnumericsentropy dissipationoptimal transport

Mathematics Subject Classification ID

Numerical investigation of stability of solutions to ordinary differential equations (65L07) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (9)

A Continuation Multiple Shooting Method for Wasserstein Geodesic Equation ⋮ Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation ⋮ A structure-preserving finite element discretization for the time-dependent Nernst-Planck equation ⋮ Entropy dissipation of Fokker-Planck equations on graphs ⋮ An Entropic Method for Discrete Systems with Gibbs Entropy ⋮ Equilibrium Selection via Optimal Transport ⋮ Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula ⋮ Fisher information regularization schemes for Wasserstein gradient flows ⋮ The Łojasiewicz inequality for free energy functionals on a graph

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A new model for realistic random perturbations of stochastic oscillators
• Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities
• Numerical study of a particle method for gradient flows
• Gradient flows of the entropy for finite Markov chains
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• A non-Maxwellian steady distribution for one-dimensional granular media
• Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
• Entropy dissipation of Fokker-Planck equations on graphs
• Ricci curvature of finite Markov chains via convexity of the entropy
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• Fokker-Planck equations for a free energy functional or Markov process on a graph
• A practical difference scheme for Fokker-Planck equations
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
• Numerical Analysis of Conservative and Entropy Schemes for the Fokker--Planck--Landau Equation
• The Variational Formulation of the Fokker--Planck Equation
• A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
• Optimal Transport
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

This page was built for publication: Entropy dissipation semi-discretization schemes for Fokker-Planck equations