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On the effective interfacial resistance through rough surfaces

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  • 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.
    Mathematics Subject Classification: 35B27, 35L05.


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