6 papers · 1 filter
Lyapunov estimates for non-factorised kinetic Fokker-Planck equations under weak spatial confinements
Émeric Bouin
In this paper, we construct weak Lyapunov functionals for kinetic Fokker-Planck equations with weak external confinements. This problem has remained widely open in the existing lit…
Nonlinear kinetic Fokker-Planck equations: existence and diffusion limits
Emeric Bouin, Jean Dolbeault, Antoine Mellet
In this paper, we focus on a new type of non-linear kinetic Fokker-Planck equation where the non-linearity comes from a non-linear diffusion in the velocity variable. The existence…
Convergence to a non-explicit steady state in non-factorized kinetic Fokker-Planck equations with (very) weak velocity confinements
Emeric Bouin, Luca Ziviani
In this article, we prove some convergence results for kinetic Fokker-Planck equations with strong space confinement but fat-tailed local equilibria and non-explicit global steady…
Sharp exponent of acceleration in general nonlocal equations with a weak Allee effect
Emeric Bouin, Jérôme Coville, Guillaume Legendre
We study an acceleration phenomenon arising in monostable integro-differential equations with a weak Allee effect. Previous works have shown its occurrence and have given correct u…
Travelling waves in non-local reaction-dispersion equations with diffuse levy measures
Emeric Bouin, Jérôme Coville
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very…
Acceleration or finite speed propagation in integro-differential equations with logarithmic Allee effect
Emeric Bouin, Jérôme Coville, Xi Zhang
This paper is devoted to studying propagation phenomena in integro-differential equations with a weakly degenerate non-linearity. The reaction term can be seen as an intermediate b…