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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 obtain the existence, uniqueness and regularity results for solutions to kinetic Fokker-Planck equations with bounded measurable coefficients in the presence of boundary conditions, including the inflow, diffuse reflection and specular…

New kind of differential equations, called local fractional differential equations, has been proposed for the first time. They involve local fractional derivatives introduced recently. Such equations appear to be suitable to deal with…

We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…

We describe the structure of solutions of the kinetic Fokker-Planck equations in domains with boundaries near the singular set in one-space dimension. We study in particular the behaviour of the solutions of this equation for inelastic…

It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion processes. In contrast to previous such results, it is not…

We study the Cauchy problem for Fokker--Planck--Kolmogorov equations with unbounded and degenerate coefficients. Sufficient conditions for the existence and uniqueness of solutions are indicated.

We develop a new method to solve the Fokker-Planck or Kolmogorov's forward equation that governs the time evolution of the joint probability density function of a continuous-time stochastic nonlinear system. Numerical solution of this…

We obtain local Holder continuity estimates up to the boundary for a kinetic Fokker-Planck equation with rough coefficients, with the prescribed influx boundary condition. Our result extends some recent developments that incorporate De…

In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the non-negativity of the solution, conserves the mass and, as the discretization parameters tend to zero,…

We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by…

A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the…

The Fokker-Planck Equation, applied to transport processes in fusion plasmas, can model several anomalous features, including uphill transport, scaling of confinement time with system size, and convective propagation of externally induced…

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 consider a Markov process on a Riemannian manifold, which solves a stochastic differential equation in the interior of the manifold and jumps according to a deterministic reset map when it reaches the boundary. We derive a partial…

We establish sharp boundary regularity results for solutions to kinetic Fokker-Planck equations under prescribed inflow boundary conditions, providing precise quantification of the boundary hypoelliptic regularization effect. For equations…

The dynamics of quantum field theories on bounded domains requires the introduction of boundary conditions on the quantum fields. We address the problem from a very general perspective by using charge conservation as a fundamental principle…

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to…

We consider a stochastic differential equation in a Hilbert space with time-dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, existence and uniqueness of a measure…

A popular approach to modeling bimolecular reactions between diffusing molecules is through the use of reactive boundary conditions. One common model is the Smoluchowski partial absorption condition, which uses a Robin boundary condition in…