Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces. (16th February 2023)

• Record Type: Journal Article
• Authors: Zanoni, Andrea
• Is Part Of: IMA journal of applied mathematics. Volume 88:Number 1(2023)
• Page Start: 67
• Page End: 101
• Publication Date: 2023-02-16
• Subjects: Langevin equation -- infinitesimal generator -- homogenization -- eigenvalue problem -- two-scale convergence -- weighted Sobolev spaces; Mathematics -- Periodicals; Mathematics; Periodicals; 519
• DOI: 10.1093/imamat/hxad003
• Languages: English
• ISSNs: 0272-4960

Abstract

Abstract: We study the homogenization of the Poisson equation with a 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.