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Raveendran, VishnuMuntean, Adrian
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Raveendran, VishnuCirillo, Emilio N. M.Muntean, Adrian
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Quarterly of Applied Mathematics
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Mathematics
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Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary dataPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2024 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485Article in journal (Refereed) Epub ahead of print
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Mathematical Society (AMS), 2024.
##### Keywords [en]

Homogenization, reaction-diffusion equations with large nonlinear drift, two-scale convergence with drift, strong convergence in moving coordinates, effective dispersion tensors for reactive flow in porous media
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:kau:diva-97991DOI: 10.1090/qam/1687ISI: 001162782500001OAI: oai:DiVA.org:kau-97991DiVA, id: diva2:1827526
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##### Funder

Swedish Research Council, 2018-03648Available from: 2024-01-14 Created: 2024-01-14 Last updated: 2024-03-08Bibliographically approved
##### In thesis

We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem.

1. Scaling effects and homogenization of reaction-diffusion problems with nonlinear drift$(function(){PrimeFaces.cw("OverlayPanel","overlay1841801",{id:"formSmash:j_idt834:0:j_idt838",widgetVar:"overlay1841801",target:"formSmash:j_idt834:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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