Related papers: Homogenization and hypocoercivity for Fokker-Planc…
In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with…
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…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…
A microscopic analysis of the viscous energy gain of energetic particles in (gradual) non-relativistic shear flows is presented. We extend previous work and derive the Fokker-Planck coefficients for the average rate of momentum change and…
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
In this paper we proceed with investigation of connections between Fokker - Planck equation and continuum mechanics. We base upon expressions from our work [2], based upon the spectral decomposition of Fokker - Planck equation solution. In…
In this paper we study the convergence of a power-law model for dilatant compressible fluids to a class of models exhibiting a maximum admissible shear rate, called thick compressible fluids. These kinds of problems were studied previously…
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties…
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…
The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…
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…
Dispersive and Strichartz estimates for solutions to general strictly hyperbolic partial differential equations with constant coefficients are considered. The global time decay estimates of $L^p-L^q$ norms of propagators are obtained, and…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a unified treatment of the available literature along with some…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
Using a simple model of self-propelled particle, the effective shear viscosity of a dilute, spatially homogeneous suspension of active particles is studied. We use formulation of non-linear Fokker-Planck equation to drive a kinetic…
In this article, basing upon probabilistic methods, we discuss periodic homogenization of a class of weakly coupled systems of linear elliptic and parabolic partial differential equations. Under the assumption that the systems have rapidly…
The Fokker--Planck equation describes the evolution of a probability distribution towards equilibrium--the flow parameter is the equilibration time. Assuming the distribution remains normalizable for all times, it is equivalent to an open…