Séminaire Editha C. Jose

Jeudi 25 Octobre 2012 (15h15)

Editha C. Jose, University of the Philippines Los Banos.

Titre : Corrector Results for a Parabolic Problem with a Memory Effect.

Résumé : The aim of this talk is to present the corrector results associated to the homogenization of a parabolic problem describing heat transfer. This work completes the earlier study on the asymptotic behaviour of a parabolic problem in a domain with two components separated by an $\varepsilon$-periodic interface.

The physical model due to Carslaw prescribes on the interface that the flux of the temperature be proportional to the jump of the temperature field by a factor of order $\varepsilon^\gamma.$ We suppose that $-1<\gamma\leq 1.$ As far as the energies of the homogenized problems are concerned, we consider the cases $-1<\gamma<1$ and $\gamma=1$ separately. To obtain the convergence of the energies, it is necessary to impose stronger assumptions on the data. The case $\gamma=1$ is the more interesting one because of the presence of a memory effect in the homogenized problem .