# Corrector results for a parabolic problem with a memory effect

Patrizia Donato; Editha C. Jose

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 3, page 421-454
- ISSN: 0764-583X

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topDonato, Patrizia, and Jose, Editha C.. "Corrector results for a parabolic problem with a memory effect." ESAIM: Mathematical Modelling and Numerical Analysis 44.3 (2010): 421-454. <http://eudml.org/doc/250829>.

@article{Donato2010,

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.
},

author = {Donato, Patrizia, Jose, Editha C.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Periodic homogenization; correctors; heat equation; interface problems; periodic homogenization; interface problem; homogeneous Dirichlet boundary condition},

language = {eng},

month = {4},

number = {3},

pages = {421-454},

publisher = {EDP Sciences},

title = {Corrector results for a parabolic problem with a memory effect},

url = {http://eudml.org/doc/250829},

volume = {44},

year = {2010},

}

TY - JOUR

AU - Donato, Patrizia

AU - Jose, Editha C.

TI - Corrector results for a parabolic problem with a memory effect

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/4//

PB - EDP Sciences

VL - 44

IS - 3

SP - 421

EP - 454

AB -
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.

LA - eng

KW - Periodic homogenization; correctors; heat equation; interface problems; periodic homogenization; interface problem; homogeneous Dirichlet boundary condition

UR - http://eudml.org/doc/250829

ER -

## References

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