Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

• DOI: 10.3390/math12142181
• Publication Date: 2024-07-11T19:59:48Z
• Authors: Yang Na; Tianjiao Men; Runmei Du; Yingjie Zhu
• Keywords: the first order necessary conditions; 0103 physical sciences; degenerate parabolic equations; nonlinear equations; QA1-939; the optimal control; 01 natural sciences; Mathematics

The optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic equations in this paper. The main result is that we deduce the first order necessary condition for the optimal control problem of nonlinear degenerate parabolic equations by variation method. Moreover, we investigate the uniqueness of the solutions to the optimal control problems. For the linear equations, we obtain the global uniqueness, while for the nonlinear equations, we obtain only the local uniqueness. Finally, we give a numerical example to validate the theoretical results.