Homogenization of a reaction–diffusion equation with Robin interface conditions

We study the asymptotic behaviour of the solution of a reaction–diffusion equation in a εε-periodic partially fractured medium with Robin interface conditions. We consider a model where the solution has a jump of order ε−1ε−1 with respect to the flux which is continuous at the interface. The macroscopic model consists of two semi-linear parabolic equations with a linear exchange term.