数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 26-32.doi: 10.1016/S0252-9602(16)30112-6

• 论文 • 上一篇    下一篇

DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES

刘振海1, 曾生达1,2   

  1. 1. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for Nationalities, Nanning 530006, China;
    2. Institute of Computer Science, Faculty of Mathematics and Computer Science Jagiellonian University, ul. Lojasiewicza 6, 30-348 Krakow, Poland
  • 收稿日期:2015-12-31 修回日期:2016-04-29 出版日期:2017-02-25 发布日期:2017-02-25
  • 通讯作者: Zhenhai LIU,E-mail:zhhliu@hotmail.com E-mail:zhhliu@hotmail.com
  • 作者简介:Shengda ZENG,E-mail:zengshengda@163.com
  • 基金资助:

    Project supported by NNSF of China (11671101), the National Science Center of Poland Under Maestro Advanced Project (UMO-2012/06/A/ST1/00262), and Special Funds of Guangxi Distinguished Experts Construction Engineering.

DIFFERENTIAL VARIATIONAL INEQUALITIES IN INFINITE BANACH SPACES

Zhenhai LIU1, Shengda ZENG1,2   

  1. 1. Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, and College of Sciences, Guangxi University for Nationalities, Nanning 530006, China;
    2. Institute of Computer Science, Faculty of Mathematics and Computer Science Jagiellonian University, ul. Lojasiewicza 6, 30-348 Krakow, Poland
  • Received:2015-12-31 Revised:2016-04-29 Online:2017-02-25 Published:2017-02-25
  • Contact: Zhenhai LIU,E-mail:zhhliu@hotmail.com E-mail:zhhliu@hotmail.com
  • About author:Shengda ZENG,E-mail:zengshengda@163.com
  • Supported by:

    Project supported by NNSF of China (11671101), the National Science Center of Poland Under Maestro Advanced Project (UMO-2012/06/A/ST1/00262), and Special Funds of Guangxi Distinguished Experts Construction Engineering.

摘要:

In this paper, we consider a new differential variational inequality (DVI, for short) which is composed of an evolution equation and a variational inequality in infinite Banach spaces. This kind of problems may be regarded as a special feedback control problem. Based on the Browder's theorem and the optimal control theory, we show the existence of solutions to the mentioned problem.

关键词: differential variational inequality, C0-semigroup, monotone operator, existence of solutions

Abstract:

In this paper, we consider a new differential variational inequality (DVI, for short) which is composed of an evolution equation and a variational inequality in infinite Banach spaces. This kind of problems may be regarded as a special feedback control problem. Based on the Browder's theorem and the optimal control theory, we show the existence of solutions to the mentioned problem.

Key words: differential variational inequality, C0-semigroup, monotone operator, existence of solutions