Communications on Pure and Applied Analysis (CPAA)

On the effective interfacial resistance through rough surfaces

Pages: 1295 - 1310, Volume 9, Issue 5, September 2010      doi:10.3934/cpaa.2010.9.1295

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Donato Patrizia - Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Avenue de l’Université, BP 12, 76801 Saint Etienne de Rouvray, France (email)
Andrey Piatnitski - Narvik University College, HiN, Postbox 385, 8505 Narvik, Norway, and, P.N. Lebedev Physical Institute RAS, Leninski prospect, 53, Moscow, 117924, Russian Federation (email)

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.

Keywords:  Homogenization, rough surfaces, interface conditions.
Mathematics Subject Classification:  35B27, 35L05.

Received: June 2009;      Revised: November 2009;      Available Online: May 2010.