Related papers: Quantitative stability estimates for Fokker-Planck…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
We consider the linear Wigner-Fokker-Planck equation subject to confining potentials which are smooth perturbations of the harmonic oscillator potential. For a certain class of perturbations we prove that the equation admits a unique…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
The Fokker-Planck equations (FPEs) for stochastic systems driven by additive symmetric $\alpha$-stable noises may not adequately describe the time evolution for the probability densities of solution paths in some practical applications,…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…
We study the well-posedness, steady states and long time behavior of solutions to Vlasov-Fokker-Planck equation with external confinement potential and nonlinear self-consistent interactions. Our analysis introduces newly characterized…
The object of this paper is the uniqueness for a $d$-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic…
We study the initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting…
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a…
We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec…
We investigate the dynamics close to a homogeneous stationary state of Vlasov equation in one dimension, in presence of a small dissipation modeled by a Fokker-Planck operator. When the stationary state is stable, we show the stochastic…
The work concerns the superposition between the Zakai equations and the Fokker-Planck equations on measure spaces. First, we prove a superposition principle for the Fokker-Planck equations on $\mR^\mN$ under the integrable condition. And…
We prove existence, uniqueness and regularity of weak solutions of Kolmogorov--Fokker--Planck equations with either local or non-local diffusion in the velocity variable and rough diffusion coefficients or kernels. Our results cover the…
We study the relaxation to equilibrium for a class linear one-dimensional Fokker-Planck equations characterized by a particular subcritical confinement potential. An interesting feature of this class of Fokker-Planck equations is that, for…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
We consider driftless stochastic differential equations and the diffusions starting from the positive half line. It is shown that the Feller test for explosions gives a necessary and sufficient condition to hold pathwise uniqueness for…
A major result concerning perturbations of integrable Hamiltonian systems is given by Nekhoroshev estimates, which ensures exponential stability of all solutions provided the system is analytic and the integrable Hamiltonian not too…
This paper concerns the proof of the exponential rate of convergence of the solution of a Fokker-Planck equation, with a drift term not being the gradient of a potential function and endowed by Robin type boundary conditions. This kind of…
This work is devoted to studying complex dynamical systems under non-Gaussian fluctuations. We first estimate the Kantorovich-Rubinstein distance for solutions of non-local Fokker-Planck equations associated with stochastic differential…