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.
Mots-clés : periodic homogenization, correctors, heat equation, interface problems
@article{M2AN_2010__44_3_421_0,
author = {Donato, Patrizia and Jose, Editha C.},
title = {Corrector results for a parabolic problem with a memory effect},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {421--454},
publisher = {EDP-Sciences},
volume = {44},
number = {3},
year = {2010},
doi = {10.1051/m2an/2010008},
mrnumber = {2666650},
zbl = {1195.35038},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010008/}
}
TY - JOUR AU - Donato, Patrizia AU - Jose, Editha C. TI - Corrector results for a parabolic problem with a memory effect JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 421 EP - 454 VL - 44 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010008/ DO - 10.1051/m2an/2010008 LA - en ID - M2AN_2010__44_3_421_0 ER -
%0 Journal Article %A Donato, Patrizia %A Jose, Editha C. %T Corrector results for a parabolic problem with a memory effect %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 421-454 %V 44 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010008/ %R 10.1051/m2an/2010008 %G en %F M2AN_2010__44_3_421_0
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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