The role of a strong confining potential in a nonlinear Fokker-Planck equation

DOI10.1016/j.na.2019.03.003zbMath1442.35023arXiv1807.11055OpenAlexW2963255288MaRDI QIDQ1985854

Luca Alasio, Maria Bruna, José Antonio Carrillo

Publication date: 7 April 2020

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.11055

zbMATH Keywords

degenerate diffusionFokker-Planck equationsnonlocal modelsstrong confinement

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Fokker-Planck equations (35Q84)

Related Items (3)

A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling ⋮ The nonlocal-interaction equation near attracting manifolds ⋮ Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds

Cites Work

• Unnamed Item
• Some variants of the classical Aubin-Lions lemma
• A nonlocal continuum model for biological aggregation
• Continuous limit of a crowd motion and herding model: analysis and numerical simulations
• Functional inequalities, thick tails and asymptotics for the critical mass Patlak-Keller-Segel model
• Contractions in the 2-Wasserstein length space and thermalization of granular media
• Kinetic models of opinion formation
• Volume effects in the Keller--Segel model: energy estimates preventing blow-up
• Double milling in self-propelled swarms from kinetic theory
• A user's guide to PDE models for chemotaxis
• Quasilinear elliptic-parabolic differential equations
• A non-Maxwellian steady distribution for one-dimensional granular media
• A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• A note on Aubin-Lions-Dubinskiĭ lemmas
• Formation of clumps and patches in self-aggregation of finite-size particles
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• 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 Fokker-Planck type approximation of parabolic PDEs with oblique boundary data
• Exponential convergence toward equilibrium for homogeneous Fokker-Planck-type equations
• A kinetic equation for granular media
• The Variational Formulation of the Fokker--Planck Equation
• Stability estimates for systems with small cross-diffusion
• Diffusion of Particles with Short-Range Interactions
• The Geometry of Diffusing and Self-Attracting Particles in a One-Dimensional Fair-Competition Regime
• Zoology of a Nonlocal Cross-Diffusion Model for Two Species
• Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations
• A Finite Volume Scheme for Nonlinear Degenerate Parabolic Equations
• A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

This page was built for publication: The role of a strong confining potential in a nonlinear Fokker-Planck equation