External Optimal Control of the Semilinear Fractional Parabolic Coupled System
研究由半线性分数阶抛物方程和抛物方程耦合系统控制的外部最优控制问题，在非线性假设下证明了系统的适定性和有界性，并建立了最优控制解的存在性和一阶必要条件。
This paper deals with an external optimal control problem governed by coupled system of semilinear fractional parabolic equation and parabolic equation with Neumann exterior value condition. Under some assumptions on the nonlinearity, the well-posedness and boundedness of solutions for the system are proved. After showing the Lipschitz continuity and Fréchet differentiability of the control-to-state operator for the controlled system, we establish the existence theorem of solutions and the first-order necessary optimality conditions for an associated optimal control problem.