φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations
type: Item
instance of: scholarly article
title: φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations
zbMATH Open document ID: 1411.82032
DOI: 10.1142/S0218202518500574
author: Jean Dolbeault
author: Xingyu Li
publication date: 2019-03-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/1712.09897
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 35Q83
Mathematics Subject Classification ID: 35Q84
zbMATH DE Number: 7042898
zbMATH Keywords: hypocoercivity
zbMATH Keywords: linear kinetic equations
zbMATH Keywords: Fokker-Planck operator
zbMATH Keywords: transport operator
zbMATH Keywords: diffusion limit
zbMATH Keywords: confinement
zbMATH Keywords: spectral gap
zbMATH Keywords: Poincaré inequality
MaRDI profile type: Publication
arXiv ID: 1712.09897
cites work: On Linear Hypocoercive BGK Models
cites work: Large-time behavior in non-symmetric Fokker-Planck equations
cites work: On logarithmic Sobolev inequalities. With a preface of Dominique Bakry and Michel Ledoux
cites work: Interpolation between logarithmic Sobolev and Poincaré inequalities
cites work: Refined convex Sobolev inequalities
cites work: ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
cites work: Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré
cites work: Q5186515
cites work: Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
cites work: Sobolev inequalities for probability measures on the real line
cites work: Convex Sobolev inequalities and spectral gap
cites work: A QUALITATIVE STUDY OF LINEAR DRIFT-DIFFUSION EQUATIONS WITH TIME-DEPENDENT OR DEGENERATE COEFFICIENTS
cites work: Bakry-Émery meet Villani
cites work: A Generalized Poincare Inequality for Gaussian Measures
cites work: Stochastic Stokes' Drift, Homogenized Functional Inequalities, and Large Time Behavior of Brownian Ratchets
cites work: Lyapunov functionals for boundary-driven nonlinear drift-diffusion equations
cites work: Phi-entropy inequalities for diffusion semigroups
cites work: Q3980859
cites work: Existence and uniqueness of a global smooth solution for the Vlasov- Poisson-Fokker-Planck system in three dimensions
cites work: Hypocoercivity without confinement
cites work: Nonlinear Stability in Lp for a Confined System of Charged Particles
cites work: On the long-time behavior of the quantum Fokker-Planck equation
cites work: Entropies, convexity, and functional inequalities: on \(\Phi\)-entropies and \(\Phi\)-Sobolev inequalities
cites work: Q5539510
cites work: Information Theory
cites work: Improved interpolation inequalities on the sphere
cites work: Uniqueness and rigidity in nonlinear elliptic equations, interpolation inequalities, and spectral estimates
cites work: Hypocoercivity for kinetic equations with linear relaxation terms
cites work: Hypocoercivity for linear kinetic equations conserving mass
cites work: A new class of transport distances between measures
cites work: On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
cites work: From Poincaré to Logarithmic Sobolev Inequalities: A Gradient Flow Approach
cites work: Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays
cites work: Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities
cites work: Spectral properties of hypoelliptic operators
cites work: Partially Alternate Derivation of a Result of Nelson
cites work: The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
cites work: Q3470840
cites work: Logarithmic Sobolev Inequalities
cites work: Q4039929
cites work: Hypoelliptic estimates and spectral theory for Fokker-Planck operators and Witten Laplacians
cites work: Q5479970
cites work: Short and long time behavior of the Fokker-Planck equation in a confining potential and applications
cites work: Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
cites work: Logarithmic Sobolev inequalities and stochastic Ising models
cites work: Hypoelliptic second order differential equations
cites work: Convergence rates for nonequilibrium Langevin dynamics
cites work: On Equations of Brownian Motion
cites work: On the Optimum Rate of Transmitting Information
cites work: Zufällige Bewegungen. (Zur Theorie der Brownschen Bewegung.)
cites work: Q2702147
cites work: Sharp Harnack inequalities for a family of hypoelliptic diffusions
cites work: On \(\mathcal{H}^1\) and entropic convergence for contractive PDMP

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φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations (OpenAlex ID)
OpenAlex ID: W2888706989

φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations (published in)
published in: M\(^3\)AS. Mathematical Models \& Methods in Applied Sciences