Related papers: Propagator norm and sharp decay estimates for Fokk…
The systematic expansion method of the solution of the Fokker-Planck equation is developed by generalizing the formulation proposed in [J. Phys. A50, 325001 (2017)]. Using this method, we obtain a new formula to calculate the mean work…
Due to its parabolic character, the diffusion equation exhibits instantaneous spatial spreading, and becomes unstable when Lorentz-boosted. According to the conventional interpretation, these features reflect a fundamental incompatibility…
Fokker-Planck equations (forward Kolmogorov equations) evolve probability densities in time from an initial condition. For distributions over the real line, these evolution equations can sometimes be transformed into dynamics over the…
The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates…
The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration and GMRES.…
We first prove a homogenization result for the fundamental solution of the linear kinetic Fokker Planck equation. We show that this solution converges, in an averaged $L^2$ sense, to the fundamental solution of an effective heat equation…
We study some jumping SDE and the corresponding Fokker-Planck (or Kolmogorov forward) equation, which is a non-local PDE. We assume only some measurability and growth conditions on the coefficients. We prove that for any weak solution…
In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker-Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces.…
Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the…
We demonstrate the equivalence of a Non--Markovian evolution equation with a linear memory--coupling and a Fokker--Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to…
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…
Anomalous subdiffusion characterizes transport in diverse physical systems and is especially prevalent inside biological cells. In cell biology, the prevailing model for chemical activation rates has recently changed from the first passage…
The Vlasov-Nordstr\"{o}m-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We prove the convergence of a modified Jordan--Kinderlehrer--Otto scheme to a solution to the Fokker--Planck equation in $\Omega \Subset \mathbb R^d$ with general -- strictly positive and temporally constant -- Dirichlet boundary…
We analyse a bidimensional nonlinear Fokker-Planck equation by considering an anisotropic case, whose diffusion coefficients are $D_x \propto |x|^{-\theta}$ and $D_y \propto |y|^{-\gamma}$ with $\theta, \gamma \in {\cal{R}}$. In this…
We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…
We consider finite-volume approximations of Fokker-Planck equations on bounded convex domains in $\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker-Planck…
This paper is devoted to $\phi$-entropies applied to Fokker-Planck and kinetic Fokker-Planck equations in the whole space, with confinement. The so-called $\phi$-entropies are Lyapunov functionals which typically interpolate between Gibbs…
We study the rate of convergence to equilibrium of the solutions to Fokker-Planck type equations with linear drift by means of Cram\'er and Energy distances, which have been recently widely used in problems related to AI, in particular for…