Mathematics (Jul 2024)

Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations

  • Yang Na,
  • Tianjiao Men,
  • Runmei Du,
  • Yingjie Zhu

DOI
https://doi.org/10.3390/math12142181
Journal volume & issue
Vol. 12, no. 14
p. 2181

Abstract

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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.

Keywords