Solutions to the seepage face model for dual porosity flows with hysteresis

This paper is concerned with theoretical analysis of the initial-boundary value problem for the dual porosity model of Darcian flows with the Preisach hysteresis operator. Due to the presence of the so-called unilateral boundary condition, the problem comes as an evolution variational inequality. We apply the penalty method to prove the global-in-time existence of the variational solution by constructing approximate solutions satisfying suitable energy type estimates.