Corrector results for a parabolic problem with a memory effect
ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 3, pp. 421-454.

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.

DOI : 10.1051/m2an/2010008
Classification : 35B27, 35K20, 82B24
Mots clés : periodic homogenization, correctors, heat equation, interface problems
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Donato, Patrizia; Jose, Editha C. Corrector results for a parabolic problem with a memory effect. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 3, pp. 421-454. doi : 10.1051/m2an/2010008. http://www.numdam.org/articles/10.1051/m2an/2010008/

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