External Optimal Control of the Semilinear Fractional Parabolic Coupled System

Jun Lei () and Wei Wei ()
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Jun Lei: Guizhou Education University
Wei Wei: Guizhou Education University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 15, 31 pages

Abstract: Abstract 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.

Keywords: Fractional parabolic equation; Optimal control; Weak solution; External control; Coupled system; 49J20; 49K20; 35S15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02611-w

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