Effective thermal conduction of a Signorini-type problem in composites with rough interface

We analyse the effect of a Signorini-type interface condition on the asymptotic behaviour, as ε tends to zero, of a problem posed in an open-bounded cylinder of (Formula presented.), (Formula presented.), divided into two connected components by an imperfect rough surface. The Signorini-type condition is expressed by means of two complementary equalities involving the jump of the solution on the interface and its conormal derivative via a parameter γ. Different limit problems are obtained according to the values of γ and the amplitude of interface oscillations.