Related papers: Homogenization and hypocoercivity for Fokker-Planc…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
We investigate the influence of a shear flow on the process of nucleation. Mesoscopic nonequilibrium thermodynamics is used to derive the Fokker-Planck equation governing the evolution of the cluster size distribution in a metastable phase…
We study the long time behavior of an Ornstein-Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian…
We study the homogenization problem for a system of stochastic differential equation with local time terms that models a multivariate diffusion in presence of semipermeable hyperplane interfaces with oblique penetration. We show that this…
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
We are concerned with the short- and large-time behavior of the $L^2$-propagator norm of Fokker-Planck equations with linear drift, i.e. $\partial_t f=\mathrm{div}_{x}{(D \nabla_x f+Cxf)}$. With a coordinate transformation these equations…
This paper is devoted to the homogenization of weakly coupled cooperative parabolic systems in strong convection regime with purely periodic coefficients. Our approach is to factor out oscillations from the solution via principal…
In this paper we proceed with investigation of connections between Fokker - Planck equation and continuum mechanics. In spectral decomposition of Fokker - Planck equation solution we preserve only terms with the smallest degree of damping.…
We investigate the Cauchy problem and the diffusion asymptotics for a spatially inhomogeneous kinetic model associated to a nonlinear Fokker-Planck operator. We derive the global well-posedness result with instantaneous smoothness effect,…
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 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…
Hypocoercivity methods are applied to linear kinetic equations without any space confinement, when local equilibria have a sub-exponential decay. By Nash type estimates, global rates of decay are obtained, which reflect the behavior of the…
The Fokker-Planck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the Fokker-Planck equation picks up a tensorial…
We consider Fokker-Planck equations in the whole Euclidean space, driven by Levy processes, under the action of confining drifts, as in the classical Ornstein-Ulhenbeck model. We introduce a new PDE method to get exponential or…
In a previous work [math.AP/0305408] three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the…
In this paper, we mainly study the large time behavior to a 2D micro-macro model for compressible polymeric fluids with small initial data. This model is a coupling of isentropic compressible Navier-Stokes equations with a nonlinear…
The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…