The Fokker-Planck equation with subcritical confinement force

DOI10.1016/j.matpur.2021.04.007zbMath1491.35415arXiv1512.07005OpenAlexW3151796744MaRDI QIDQ2036831

Otared Kavian, Mamadou Ndao, Stéphane Mischler

Publication date: 30 June 2021

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.07005

zbMATH Keywords

Fokker-Planck equationsemigroupspectral gapweak Poincaré inequalityKrein-Rutman theoremweak dissipativity

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) One-parameter semigroups and linear evolution equations (47D06) Estimates of eigenvalues in context of PDEs (35P15) Fokker-Planck equations (35Q84)

Related Items (8)

Convergence rate to equilibrium for collisionless transport equations with diffuse boundary operators: a new tauberian approach ⋮ Time averages for kinetic Fokker-Planck equations ⋮ Harris-type results on geometric and subgeometric convergence to equilibrium for stochastic semigroups ⋮ Decay rates of convergence for Fokker-Planck equations with confining drift ⋮ Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition ⋮ Chemotaxis and reactions in biology ⋮ Fractional Fokker--Planck Equation with General Confinement Force ⋮ Fractional hypocoercivity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a kinetic FitzHugh-Nagumo model of neuronal network
• Spectral analysis of semigroups and growth-fragmentation equations
• Exponential stability of slowly decaying solutions to the kinetic-Fokker-Planck equation
• On the speed of approach to equilibrium for a collisionless gas
• Regularity, local behavior and partial uniqueness for self-similar profiles of Smoluchowski's coagulation equation
• On the Boltzmann equation for diffusively excited granular media
• Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
• An introduction to Sobolev spaces and interpolation spaces
• Functional inequalities for heavy tailed distributions and application to isoperimetry
• Subgeometric rates of convergence of \(f\)-ergodic strong Markov processes
• Non-uniform stability for bounded semi-groups on Banach spaces
• A simple proof of the Poincaré inequality for a large class of probability measures
• One-parameter semigroups of positive operators
• A perturbation theorem for the essential spectral radius of strongly continuous semigroups
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• The Boltzmann equation with a soft potential. II: Nonlinear, spatially- periodic
• \(L_ 2\) rates of convergence for attractive reversible nearest particle systems: The critical case
• On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds.
• Landau equation for very soft and Coulomb potentials near maxwellians
• On self-similarity and stationary problem for fragmentation and coagulation models.
• Some remarks on ultracontractivity
• The Landau equation in a periodic box
• Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré
• General relative entropy inequality: an illustration on growth models
• Polynomial stability of operator semigroups
• Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

This page was built for publication: The Fokker-Planck equation with subcritical confinement force