We obtain equilibration rates for a one-dimensional nonlocal Fokker–Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of large swarm robots, feeling each other in terms their distance, towards steady profile characterized by uniform spreading over finite interval line. The result follows combining entropy methods quantifying decay solution its quasi-st...

We study the long time behavior of kinetic Fokker-Planck equation with mean field interaction, whose limit is often called Vlasov-Fokker-Planck equation. prove a uniform (in number particles) exponential convergence to equilibrium for solutions in weighted Sobolev space H1(?) rate which explicitly computable and independent particles. The originality proof relies on functional inequalities hypo...

We construct a kind of thermal potential and then put the black hole thermodynamic system in it. In this regard, some properties are related to geometric characteristics potential. Driven by intrinsic fluctuations, behavior is stochastic. With help solving Fokker-Planck equation analytically, we obtain discrete energy spectrum Schwarzschild Banados-Teitelboim-Zanelli (BTZ) holes For hole, propo...

We investigate the long time/small mean-free-path asymptotic behavior of the solutions of a Vlasov-Lévy-Fokker-Planck equation and show that the asymptotic dynamics for the VLFP are described by an anomalous diffusion equation.