Bilinear Optimal Control of a Nonlinear Chemotaxis Equations
In this paper,we study the bilinear optimal control of a nonlinear chemotaxis equations.The paper firstly proves the existence uniqueness of the strong solution of the parabolic system of equations by employing the Leray-Schauder fixed point theorem.Secondly,we discusses the existence of the optimal control by means of the minimization sequence.Finally,we establishes the variational inequality and derives the first-order necessary condition by the Fréchet differentiability of the control-to-state operator L.
Keller-Segel modelOptimal controlLeray-Schauder fixed point theoremNecessary optimality conditions
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