Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains
Victor A. Kovtunenko, Sina Reichelt, Anna V. Zubkova · Mathematical Methods in the Applied Sciences · 2019
This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions. In the variational setting of the problem, we prove the homogenization theorem and a bidomain averaged model. The periodic unfolding technique is used to obtain the residual error estimate with a first-order corrector.