Diffusion with very weak confinement

2019/01/24 by Émeric Bouin, Jean Dolbeault, Bouin, Emeric +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1901.08323

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to Fokker-Planck and linear kinetic equations with very weak confinement corresponding to a potential with an at most logarithmic growth and no integrable stationary state. Our goal is to understand how to measure the decay rates when the diffusion wins over the confinement although the potential diverges at infinity.

Citations

• Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus

Related

• The kinetic Fokker-Planck equation with weak confinement force
• Convergence to a non-explicit steady state in non-factorized kinetic Fokker-Planck equations with (very) weak velocity confinements
• On a class of Fokker-Planck equations with subcritical confinement
• Decay rates of convergence for Fokker-Planck equations with confining drift
• Infinite invariant densities for anomalous diffusion in optical lattices and other logarithmic potentials