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Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

Author

Listed:
  • Yang Na

    (School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China
    School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China)

  • Tianjiao Men

    (School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China)

  • Runmei Du

    (School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China)

  • Yingjie Zhu

    (School of Mathematics and Statistics, Changchun University, Changchun 130012, China)

Abstract

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.

Suggested Citation

  • Yang Na & Tianjiao Men & Runmei Du & Yingjie Zhu, 2024. "Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations," Mathematics, MDPI, vol. 12(14), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2181-:d:1433555
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