{"title":"Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces","authors":"Andrea Zanoni","doi":"10.1093/imamat/hxad003","DOIUrl":null,"url":null,"abstract":"\n 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.","PeriodicalId":56297,"journal":{"name":"IMA Journal of Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imamat/hxad003","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The IMA Journal of Applied Mathematics is a direct successor of the Journal of the Institute of Mathematics and its Applications which was started in 1965. It is an interdisciplinary journal that publishes research on mathematics arising in the physical sciences and engineering as well as suitable articles in the life sciences, social sciences, and finance. Submissions should address interesting and challenging mathematical problems arising in applications. A good balance between the development of the application(s) and the analysis is expected. Papers that either use established methods to address solved problems or that present analysis in the absence of applications will not be considered.
The journal welcomes submissions in many research areas. Examples are: continuum mechanics materials science and elasticity, including boundary layer theory, combustion, complex flows and soft matter, electrohydrodynamics and magnetohydrodynamics, geophysical flows, granular flows, interfacial and free surface flows, vortex dynamics; elasticity theory; linear and nonlinear wave propagation, nonlinear optics and photonics; inverse problems; applied dynamical systems and nonlinear systems; mathematical physics; stochastic differential equations and stochastic dynamics; network science; industrial applications.
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