The Fokker--Planck Equation with Absorbing Boundary Conditions in Bounded Domains

DOI10.1137/16M1109928zbMath1392.35313OpenAlexW2801347329WikidataQ129963344 ScholiaQ129963344MaRDI QIDQ4637760

Hyung-Ju Hwang, Juhi Jang, Jaewoo Jung

Publication date: 26 April 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1109928

zbMATH Keywords

maximum principleinitial-boundary value problemexistence of weak solutionFokker-Planck equationfundamental solutionHölder continuitysingular setabsorbing boundaryexistence of mild solutionbackward Fokker-Planck equationboundary hypoellipticityregularized Fokker-Planck equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Variational methods applied to PDEs (35A15) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Fokker-Planck equations (35Q84) Classical solutions to PDEs (35A09)

Related Items

Trend to equilibrium for the kinetic Fokker-Planck equation via the neural network approach ⋮ A probabilistic study of the kinetic Fokker-Planck equation in cylindrical domains ⋮ On the structure of the singular set for the kinetic Fokker–Planck equations in domains with boundaries ⋮ Kinetic models for semiflexible polymers in a half-plane ⋮ Analysis of absorbing boundary conditions for the anomalous diffusion in comb model on unbounded domain by finite volume method ⋮ COMPOSITE LAGUERRE PSEUDOSPECTRAL METHOD FOR FOKKER-PLANCK EQUATIONS ⋮ Pencil-Beam Approximation of Stationary Fokker--Planck ⋮ Nonuniqueness for the kinetic Fokker-Planck equation with inelastic boundary conditions ⋮ The Landau equation with the specular reflection boundary condition ⋮ The model reduction of the Vlasov–Poisson–Fokker–Planck system to the Poisson–Nernst–Planck system via the Deep Neural Network Approach ⋮ Explicit structure of the Fokker-Planck equation with potential ⋮ Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition ⋮ Stable and Efficient Petrov--Galerkin Methods for a Kinetic Fokker--Planck Equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A high order moment method simulating evaporation and advection of a polydisperse liquid spray
• Regularity of the Boltzmann equation in convex domains
• On a relativistic Fokker-Planck equation in kinetic theory
• Chemical kinetics and diffusion approach: the history of the Klein-Kramers equation
• Formation and propagation of discontinuity for Boltzmann equation in non-convex domains
• The Fokker-Planck equation with absorbing boundary conditions
• Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
• Global existence for the Vlasov-Poisson system in bounded domains
• On the existence of global weak solutions for Vlasov-Poisson-Fokker- Planck systems
• Generic global classical solutions of the Vlasov-Fokker-Planck-Poisson system in three dimensions
• A variational principle for the Kramers equation with unbounded external forces
• Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
• Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system
• The Fokker-Planck equation. Methods of solutions and applications.
• Regular solutions of the Vlasov-Poisson-Fokker-Planck system.
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• Smoothing effect for the nonlinear Vlasov-Poisson-Fokker-Planck system
• Singular solutions of the Vlasov-Maxwell system on a half line
• On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
• Well-posedness of the Fokker-Planck equation in a scattering process
• Hypoelliptic second order differential equations
• On the kinetic Fokker-Planck equation in the half-space with absorbing barriers
• Kinetic equations with Maxwell boundary conditions
• Hypocoercivity
• A drop of ink falls from my pen. . . it comes to earth, I know not when
• Global weak solutions for the initial-boundary-value problems Vlasov-Poisson-Fokker-Planck System
• Long-time behaviour for solutions of the Vlasov-Poisson-Fokker-Planck equation
• Asymptotic Behavior of an Initial-Boundary Value Problem for the Vlasov--Poisson--Fokker--Planck System
• The Variational Formulation of the Fokker--Planck Equation
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
• Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries
• Regularity for the Vlasov--Poisson System in a Convex Domain
• On the initial value problem for the Vlasov‐Poisson‐Fokker‐Planck system with initial data in L^p spaces
• The Fundamental Solution of a Degenerate Partial Differential Equation of Parabolic Type
• Random Walk in the Presence of Absorbing Barriers
• Stochastic Problems in Physics and Astronomy
• Brownian motion in a field of force and the diffusion model of chemical reactions