Modelling and control of natural convection in canned foods

In this paper we study mathematically an industrial problemrelated to sterilization processes involving heat transfer bynatural convection. We give results of existence and regularityfor the solution of this problem. We recast the whole problemas an optimal control problem with pointwise constraints onthe state and the control in order to ensure the reduction ofmicroorganism concentration and the retention of nutrients,and to save energy. Finally, we give results on existence ofthe optimal solution and optimality conditions for its characterization.