Asymptotic Expansion of Steady-State Potential in a High Contrast Medium with a Thin Resistive Layer

We study the steady-state potential in a high contrast medium with a resistive thin layer. We provide asymptotic expansion of the potential at any order. Transmission conditions at any order and the corresponding variational formulation are given. We prove uniform estimates with respect to the thickness of the layer and with respect to its resistivity. The main insight consists in the uniform variational formulation whatever small the layer conductivity is. Numerical simulations illustrate the theoretical results.Modélisation multi-échelle de l'électroporation validée par les expérience