We consider a nonlinear reaction–diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order , and the equation inside the layer depends on the parameter . We consider the critical scaling of the diffusion coefficients in the channels and nonlinear Neumann-boundary condition on the channels’ lateral boundaries. We derive effective models in the limit , when the channel-domain is replaced by an interface between the two bulk-domains. Due to the critical size of the diffusion coefficients, we obtain jumps for the solution and its normal fluxes across , involving the solutions of local cell problems on the reference channel in every point of the interface . This is a joint work with Markus Gahn (University of Heidelberg)
