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Homogenization and concentration for a diffusion equation with large convection in a bounded domain
Ecole Polytechnique, Palaiseau Cedex, France.
Narvik University College, Narvik, Norway.
Lebedev Physical Institute RAS, Moscow, Russia.
2012 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 262, no 1, p. 300-330Article in journal (Refereed) Published
Abstract [en]

We consider the homogenization of a non-stationary convection–diffusion equation posed in a bounded domain with periodically oscillating coefficients and homogeneous Dirichlet boundary conditions. Assuming that the convection term is large, we give the asymptotic profile of the solution and determine its rate of decay. In particular, it allows us to characterize the “hot spot”, i.e., the precise asymptotic location of the solution maximum which lies close to the domain boundary and is also the point of concentration. Due to the competition between convection and diffusion, the position of the “hot spot” is not always intuitive as exemplified in some numerical tests.

Place, publisher, year, edition, pages
2012. Vol. 262, no 1, p. 300-330
Keywords [en]
Homogenization, Convection–diffusion, Localization
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-27154DOI: 10.1016/j.jfa.2011.09.014OAI: oai:DiVA.org:hig-27154DiVA, id: diva2:1222159
Available from: 2018-06-21 Created: 2018-06-21 Last updated: 2018-06-21Bibliographically approved

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Pankratova, Iryna

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