Nonlocal Approximations to Fokker-Planck Equations
نویسندگان
چکیده
منابع مشابه
Generalized Stochastic Fokker-Planck Equations
We consider a system of Brownian particles with long-range interactions. We go beyond the mean field approximation and take fluctuations into account. We introduce a new class of stochastic Fokker-Planck equations associated with a generalized thermodynamical formalism. Generalized thermodynamics arises in the case of complex systems experiencing small-scale constraints. In the limit of short-r...
متن کاملPhi-entropy inequalities and Fokker-Planck equations
We present new Φ-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given.
متن کاملRate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control
The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a timedependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and prove that the dynamics in the small-parameter limit can be described by a rate-independent ...
متن کاملProbabilistic representation for solutions to nonlinear Fokker–Planck equations
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker–Planck equation in Rd with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear stochastic differential equation. The case of a nonlinear Fokker–Planck equation with linear space dependent drift is also studied.
متن کاملConvergence to equilibrium in Wasserstein distance for Fokker-Planck equations
We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Funkcialaj Ekvacioj
سال: 2019
ISSN: 0532-8721
DOI: 10.1619/fesi.62.35