Application of the $j$-subgradient in a problem of electropermeabilisation

We study a coupled elliptic-parabolic Poincar'e-Steklov system arising in electrical cell activity in biological tissues. By using the notion of $j$-subgradient, we show that this system has a gradient structure and thus obtain wellposedness. We further exploit the gradient structure for the discretisation of the problem and provide numerical experiments.