On the effective interfacial resistance through rough surfaces

Donato Patrizia; Andrey Piatnitski

doi:10.3934/cpaa.2010.9.1295

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2010, Volume 9, Issue 5: 1295-1310. Doi: 10.3934/cpaa.2010.9.1295

This issue Previous Article An overview on some results concerning the transport equation and its applications to conservation laws Next Article On the regularity of minimizers to degenerate functionals

On the effective interfacial resistance through rough surfaces

Donato Patrizia^1, and
Andrey Piatnitski^2,

1.
Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Avenue de l’Université, BP 12, 76801 Saint Etienne de Rouvray
2.
Narvik University College, HiN, Postbox 385, 8505 Narvik, Norway, and, P.N. Lebedev Physical Institute RAS, Leninski prospect, 53, Moscow, 117924

Received: May 31, 2009

Revised: October 31, 2009

Published: August 2010

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Abstract

The paper deals with homogenization of an elliptic boundary value problem stated in a domain which consists of two connected components separated by a rapidly oscillating interface with a periodic microstructure, the interface being situated in a small neighbourhood of a hyperplane. At the interface we suppose the following transmission conditions: (i) the flux is continuous, (ii) the jump of a solution at the interface is proportional to the flux through the interface.
We derive the homogenized problem and effective transmission condition for different values of the ratio between the microstructure period and the amplitude of the interface oscillations, as well as for the different values of the mentioned proportionality coefficient.

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Mathematics Subject Classification: 35B27, 35L05.

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