Corrector results for a parabolic problem with a memory effect

Issue Date

5-2010

Abstract

The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189.222] on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux of the temperature is proportional to the jump of the temperature field, by a factor of order εγ. We suppose that .1 < γ ≤ 1. As far as the energies of the homogenized problems are concerned, we consider the cases -1 < γ < 1 and γ = 1 separately. To obtain the convergence of the energies, it is necessary to impose stronger assumptions on the data. As seen in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189.222] and [Faella and Monsurrò, Topics on Mathematics for Smart Systems, World Sci. Publ., Hackensack, USA (2007) 107.121] (also in [Donato et al., J. Math. Pures Appl. 87 (2007) 119.143]), the case γ = 1 is more interesting because of the presence of a memory effect in the homogenized problem. © EDP Sciences, SMAI 2010.

Source or Periodical Title

ESAIM: Mathematical Modelling and Numerical Analysis

ISSN

0764-583X

Volume

44

Issue

3

Page

421-454

Document Type

Article

Language

English

Subject

Correctors, Heat equation, Interface problems, Periodic homogenization

Identifier

doi:10.1051/m2an/2010008.

Digital Copy

yes

Link to Full Text

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