Corrector results for a parabolic problem with a memory effect
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 3, p. 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 : https://doi.org/10.1051/m2an/2010008
Classification:  35B27,  35K20,  82B24
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {3},
     year = {2010},
     pages = {421-454},
     doi = {10.1051/m2an/2010008},
     zbl = {1195.35038},
     mrnumber = {2666650},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_3_421_0}
}
Donato, Patrizia; Jose, Editha C. Corrector results for a parabolic problem with a memory effect. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 3, pp. 421-454. doi : 10.1051/m2an/2010008. http://www.numdam.org/item/M2AN_2010__44_3_421_0/

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