Periodic solutions to a heat equation with hysteresis in the source term

This paper is concerned with a parabolic problem with hysteresis effects in the heat source, which models the feedback control. The existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time. More precisely, with the help of the subdifferential operator theory and the Poincaré map, the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage-to-limit procedure.