On the effective interfacial resistance through rough surfaces
Patrizia Donato, Andrey Lvovich Piatnitski · Communications on Pure & Applied Analysis · 2010
The paper deals with homogenization of an elliptic boundary valueproblem stated in a domain which consists of two connected components separatedby a rapidly oscillating interface with a periodic microstructure, theinterface being situated in a small neighbourhood of a hyperplane. At theinterface we suppose the following transmission conditions: (i) the flux is continuous,(ii) the jump of a solution at the interface is proportional to the fluxthrough the interface. We derive the homogenized problem and effective transmission conditionfor different values of the ratio between the microstructure period and theamplitude of the interface oscillations, as well as for the different values of thementioned proportionality coefficient.