Weak Solutions of a Reaction Diffusion Systemwith Superdiffusion and Its Optimal Control

The existence and uniqueness of weak solutions to the 2-dimensionalreaction diffusion system with superdiffusion and the optimal control of suchmodel are investigated in this paper. Fractional function spaces, Galerkin ap-proximation method and Gronwall inequality are used to obtain the existenceand uniqueness of weak solutions. On this basis, an optimal control prob-lem of such superdiffusive system is further considered by using the minimalsequence.