Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

2021/12/09 by Zanoni, Andrea · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.04921

Abstract

We study the homogenization of the Poisson equation with reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spaces in unbounded domains. We provide convergence results for the solution of the multiscale problems above to their homogenized surrogate. A series of numerical examples corroborate our analysis.

Cited by

• Nonparametric estimation of homogenized invariant measures from multiscale data via Hermite expansion

Related

• A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics
• Rough homogenization for Langevin dynamics on fluctuating Helfrich surfaces
• Stochastic homogenization of the Landau-Lifshitz-Gilbert equation
• Two-scale homogenization for a general class of high contrast PDE systems with periodic coefficients
• Homogenization of monotone parabolic problems with an arbitrary number of spatial and temporal scales