Related papers: Approximate solution for Fokker-Planck equation
We study a nonlocal approximation of the Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium in a way which does not degenerate as we approach the local limit of the equation. This uniform estimate cannot…
In this article we try to bridge the gap between the quantum dynamical semigroup and Wigner function approaches to quantum open systems. In particular we study stationary states and the long time asymptotics for the quantum Fokker-Planck…
We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. We prove the existence of an equilibrium (in the case of a general force) and we establish some (polynomial and…
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation…
We consider a particle trapped by a generic external potential and under the influence of a quantum-thermal Ohmic bath. Starting from the Langevin equation, we derive the corresponding Schwinger-Keldysh action. Then, within the…
We analyse a Fokker-Planck like equation, driven by a scalar parameter in order to reach an integral constraint. We exhibit criteria guaranteeing existence-uniqueness of a solution. We also provide counter-examples. This problem is…
In this paper we study some properties of the generalized Fokker-Planck equation induced by the time-changed fractional Ornstein-Uhlenbeck process. First of all, we exploit some sufficient conditions to show that a mild solution of such…
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together…
In this paper we present a direct perturbative method to solving certain Fokker-Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The method makes use of the connection between…
We study the existence and the uniqueness of a solution $\fy$ to the linear Fokker-Planck equation $-\Delta \fy + \div(\fy \F) = f$ in a bounded domain of $\R^d$ when $\F$ is a "confinement" vector field acting for instance like the inverse…
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the…
We present a new stability and convergence analysis for the spatial discretization of a time-fractional Fokker--Planck equation in a convex polyhedral domain, using continuous, piecewise-linear, finite elements. The forcing may depend on…
We investigate a family of generalized Fokker-Planck equations that contains Richardson and porous media equations as members. Considering a confining drift term that is related to an effective potential, we show that each equation of this…
In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…
This paper deals with the long time behavior of solutions to a "fractional Fokker-Planck" equation of the form $\partial_t f = I[f] + \text{div}(xf)$ where the operator $I$ stands for a fractional Laplacian. We prove an exponential in time…
We consider the Kramers--Smoluchowski equation at a low temperature regime and show how semiclassical techniques developed for the study of the Witten Laplacian and Fokker--Planck equation provide quantitative results. This equation comes…
We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation…
We consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation is reduced to…
We show that solutions of nonlinear nonlocal Fokker--Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly strong confining potentials defined in the whole space. Two…
We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability…