相关论文: Large-time behavior in non-symmetric Fokker-Planck…
We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is order 1 in space and if the space grid…
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…
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 consider a nonlinear Fokker-Planck equation derived from a Cucker-Smale model for flocking with noise. There is a known phase transition depending on the noise between a regime with a unique stationary solution which is isotropic…
We study the asymptotic behavior of Fokker-Planck equations with spatially inhomogeneous nonlinear diffusion, based on the energy dissipation law. First, we consider the Fokker-Planck equation with porous-medium-type nonlinear diffusion…
In this article we consider a Fokker-Planck equation with a non-local, mass preserving perturbation. We show that the perturbed Fokker-Planck operator generates a $C_0$-semigroup on an exponentially weighted $L^2$-space. Surprisingly, the…
A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of…
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 study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…
A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck…
By constructing successful couplings for degenerate diffusion processes, explicit derivative formula and Harnack type inequalities are presented for solutions to a class of degenerate Fokker-Planck equations on $\R^m\times\R^{d}$. The main…
The displacement $\lambda$-convexity of a nonstandard entropy with respect to a nonlocal transportation metric in finite state spaces is shown using a gradient flow approach. The constant $\lambda$ is computed explicitly in terms of a…
We are interested in the large-time behavior of periodic entropy solutions in $L^\infty$ to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer…
We consider the Fokker--Planck equations with irregular coefficients. Two different cases are treated: in the degenerate case, the coefficients are assumed to be weakly differentiable, while in the non-degenerate case the drift satisfies…
We introduce a class of new one-dimensional linear Fokker--Planck type equations describing the evolution in time of the wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an…
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…
We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in the production of non-woven textiles. Following a micro-macro decomposition, we use hypocoercivity…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…