Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (2): 515-530.

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Optimal Control for a Class of Nonlinear Evolutionary Equations with Weakly Continuous Operators

Zeng Biao()   

  1. College of of Mathematics and Physics, Center for Applied Mathematics of Guangxi, Nanning 530006; Guangxi University for Nationalities, Nanning 530006
  • Received:2021-08-30 Revised:2022-10-18 Online:2023-04-26 Published:2023-04-17
  • Supported by:
    NSFC(12201137);Science and Technology Innovation Talent Project of Guangxi(桂科AD21220103);Start-up Project of Scientific Research on Introducing Talents at School Level in Guangxi University for Nationalities(2019KJQD04)

Abstract:

In the paper we study an optimal control problem for a class of nonlinear evolutionary matrixs involving weakly continuous operators. By exploiting the Rothe method and using a surjectivity result for weakly continuous operators, we establish the solvability for the matrix. Then we show the existence of optimal state-control pairs for the optimal control problem. The main results are applied to non-stationary Navier-Stokes-Voigt matrix.

Key words: Evolutionary matrix, Optimal control, Weakly continuous operator, Navier-Stokes-Voigt matrix

CLC Number: 

  • O175.29
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