Homogenization of a Neutronic Critical Diffusion Problem with Drift

Advection-diffusion Problems with Rapidly Oscillating Coefficients and Large Expected Drift. Part 1: Homogenization - Existence, Uniqueness and Regularity

This contribution is concerned with the homogenization of linear advection-diffusion problems with rapidly oscillating coefficient functions and a large expected drift. Even though the homogenization of this type of problems is generally well known, there are several details that have not yet been treated explicitly or even been treated at all. In this paper we will give a survey of this topic ...

From homogenization to averaging in cellular flows

We consider an elliptic eigenvalue problem with a fast cellular flow of amplitude A, in a twodimensional domain with L cells. For fixed A, and L→∞, the problem homogenizes, and has been well studied. Also well studied is the limit when L is fixed, and A → ∞. In this case the solution equilibrates along stream lines. In this paper, we show that if both A → ∞ and L → ∞, then a transition between ...

On the Sector Condition and Homogenization of Diffusions with a Gaussian Drift

Diffusion and Homogenization approximation for semiconductor Boltzmann-Poisson system

We are concerned with the study of the diffusion and homogenization approximation of the Boltzmann-Poisson system in presence of a spatially oscillating electrostatic potential. By analyzing the relative entropy, we prove uniform energy estimate for well prepared boundary data. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Bol...

Maximum Likelihood Drift Estimation for Multiscale Diffusions

We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of fast/slow problems for which a closed coarse-grained equation for the slow variables can be rigorously derived, which we refer to as averaging and homogenizatio...