一类带有弱连续算子的发展方程的最优控制

数学物理学报 ›› 2023, Vol. 43 ›› Issue (2): 515-530.

一类带有弱连续算子的发展方程的最优控制

曾彪()

广西民族大学数学与物理学院南宁 530006；广西应用数学中心南宁 530006

收稿日期:2021-08-30 修回日期:2022-10-18 出版日期:2023-04-26 发布日期:2023-04-17
作者简介:曾彪，E-mail: biao_zeng@163.com
基金资助:
国家自然科学基金(12201137);广西科技基地和人才专项(桂科AD21220103);广西民族大学引进人才科研启动项目(2019KJQD04)

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

Zeng Biao()

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)

摘要/Abstract

摘要：

该文研究一类带有弱连续算子的发展方程的一个最优控制问题. 通过运用Rothe方法和弱连续算子的一个满射定理, 建立方程的可解性. 然后证明最优控制问题的最优状态-控制对的存在性. 最后把主要结果应用到非平稳的Navier-Stokes-Voigt方程上.

关键词: 发展方程, 最优控制, 弱连续算子, Navier-Stokes-Voigt方程

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

中图分类号:

O175.29

曾彪. 一类带有弱连续算子的发展方程的最优控制[J]. 数学物理学报, 2023, 43(2): 515-530.

Zeng Biao. Optimal Control for a Class of Nonlinear Evolutionary Equations with Weakly Continuous Operators[J]. Acta mathematica scientia,Series A, 2023, 43(2): 515-530.

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