Stability and memory effects in a homogenized model governing the electrical conduction in biological tissues

We present a macroscopic model of electrical conduction in biological tissues. This model is derived via a homogenization limit by a microscopic formulation, based on Maxwell's equations, taking into account the periodic geometry of the microstructure. We also study the asymptotic behaviour of the model for large times. Our results imply that periodic boundary data lead to an asymptotically periodic solution. The model is relevant in applications like electric impedance tomography.