相关论文: Homogenization of linear transport equations in a …

We study the problem of characterizing the effective (homogenized) properties of materials whose diffusive properties are modeled with random fields. Focusing on elliptic PDEs with stationary and ergodic random coefficient functions, we…

We analyze the convergence to equilibrium in a family of Kac-like kinetic equations in multiple space dimensions. These equations describe the change of the velocity distribution in a spatially homogeneous gas due to binary collisions…

The behavior of spinning particles in the stationary homogeneous electric field is considered and trajectories are found for various spin orientations. We study the acceleration of spinning particles by an electric field, as well as the…

The aim of this paper is to examine the large-scale behavior of dynamical optimal transport on stationary random graphs embedded in $\R^n$. Our primary contribution is a stochastic homogenization result that characterizes the effective…

We study the homogenization of an obstacle problem in a perforated domain. The holes are periodically distributed but have random size and shape. The capacity of the holes is assumed to be stationary ergodic. As in the periodic case, we…

We present a simple new proof for the stochastic homogenization of quasiconvex (level-set convex) Hamilton-Jacobi equations set in stationary ergodic environments. Our approach, which is new even in the convex case, yields more information…

We determine the asymptotic behavior of the solutions to the linear elastodynamic equations in a stratified medium comprising an alternation of possibly very stiff layers with much softer ones, when the thickness of the layers tends to…

This article addresses the homogenization of linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In…

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The…

Using a perturbative approach, an evolution equation for the space charge density, correct up to the third order, is deduced for arbitrary initial density profiles of the electron and ion fluids in a cold nonrelativistic plasma. The…

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…

We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…

We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial…

In this paper it is shown that the equations of electric field lines of an arbitrarily moving charged particle in the general case are reduced to homogeneous, linear differential equations with variable coefficients. For trajectories where…

We study homogenization for fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media from the qualitative and quantitative perspective. We show that under suitable hypotheses, solutions to fully nonlinear…

Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…

A linear stability analysis of the hydrodynamic equations of a model for confined quasi-two-dimensional granular gases is carried out. The stability analysis is performed around the homogeneous steady state (HSS) reached eventually by the…

We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains using modeling for non-periodic domains with…

In this paper, we consider stochastic homogenization of elliptic equations with unbounded and non-uniformly elliptic coefficients. Extending subadditive arguments, we get an estimate for the rate of the convergence of the solution of the…

This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…