5 papers
Nonlinear Diffusion Equations: Full characterization of Entropies
Anton Arnold, Jose A. Carrillo, Daniel Matthes
This paper is concerned with the large-time behavior of quasilinear Fokker-Planck equations with confinement on the whole space . It aims at characterizing all relati…
Long time behavior of Fokker-Planck equations for bosons and fermions
Anton Arnold, Marlies Pirner, Gayrat Toshpulatov
This paper is concerned with space inhomogeneous quantum Fokker-Planck equations posed on a classical kinetic phase space. The nonlinear factor appears both in the tran…
Trend to equilibrium and hypoelliptic regularity for the relativistic Fokker-Planck equation
Anton Arnold, Gayrat Toshpulatov
We consider the relativistic, spatially inhomogeneous Fokker-Planck equation with an external confining potential. We prove the exponential time decay of solutions towards the glob…
Exponential stability and hypoelliptic regularization for the kinetic Fokker-Planck equation with confining potential
Anton Arnold, Gayrat Toshpulatov
This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker-Planck equations with non-quadr…
Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations
Anton Arnold, Amit Einav, Tobias Wöhrer
The goal of this work is to find the sharp rate of convergence to equilibrium under the quadratic Fisher information functional for solutions to Fokker-Planck equations governed by…