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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 Name | Affiliation | | 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. |
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