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Weak Solutions of a Reaction Diffusion Systemwith Superdiffusion and Its Optimal Control
  
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KeyWord:Weak solutions  optimal control  reaction-diffusion  Riesz opera- tor
Author NameAffiliation
Biao Liu School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China 
Ranchao Wu School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China 
Liping Chen School of Electrical Engineering and Automation, Hefei University of Tech- nology, Hefei, Anhui 230009, China 
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Abstract:
      The existence and uniqueness of weak solutions to the 2-dimensional reaction diffusion system with superdiffusion and the optimal control of such model are investigated in this paper. Fractional function spaces, Galerkin ap- proximation method and Gronwall inequality are used to obtain the existence and uniqueness of weak solutions. On this basis, an optimal control prob- lem of such superdiffusive system is further considered by using the minimal sequence.