Evolutionary $\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker--Planck Equations in Multiple Dimensions
DOI10.1137/21M1410968zbMath1498.35543arXiv2008.10962OpenAlexW4285802994WikidataQ114074059 ScholiaQ114074059MaRDI QIDQ5092892
Lorenzo Portinale, Jan Maas, Dominik Forkert
Publication date: 26 July 2022
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.10962
Brownian motion (60J65) Variational methods applied to PDEs (35A15) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Fokker-Planck equations (35Q84) Optimal transportation (49Q22)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On gradient structures for Markov chains and the passage to Wasserstein gradient flows
- Entropic Ricci curvature bounds for discrete interacting systems
- Geodesic convexity of the relative entropy in reversible Markov chains
- Gradient flow structures for discrete porous medium equations
- On microscopic origins of generalized gradient structures
- Gradient flows of the entropy for finite Markov chains
- Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
- The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
- Upper bounds for symmetric Markov transition functions
- Parabolic Harnack inequality and estimates of Markov chains on graphs
- Composite media and asymptotic Dirichlet forms
- A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
- On the geometry of geodesics in discrete optimal transport
- The gradient discretisation method
- Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
- Ricci curvature of finite Markov chains via convexity of the entropy
- Effective diffusion in thin structures via generalized gradient systems and EDP-convergence
- Gradient flow formulations of discrete and continuous evolutionary models: a unifying perspective
- Homogenisation of one-dimensional discrete optimal transport
- Fokker-Planck equations for a free energy functional or Markov process on a graph
- Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry
- Modeling of chemical reaction systems with detailed balance using gradient structures
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
- Coarse-graining via EDP-convergence for linear fast-slow reaction systems
- The Brezis–Ekeland Principle for Doubly Nonlinear Equations
- The Variational Formulation of the Fokker--Planck Equation
- Gamma-convergence of gradient flows with applications to Ginzburg-Landau
- A General Integral Representation Result for Continuum Limits of Discrete Energies with Superlinear Growth
- Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator
- Coarse graining of a Fokker–Planck equation with excluded volume effects preserving the gradient flow structure
- A gradient system with a wiggly energy and relaxed EDP-convergence
- Scaling Limits of Discrete Optimal Transport
- Simulation of multiphase porous media flows with minimising movement and finite volume schemes
- Discrete Ricci curvature bounds for Bernoulli-Laplace and random transposition models
- Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence
This page was built for publication: Evolutionary $\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker--Planck Equations in Multiple Dimensions
