数学物理学报 ›› 2011, Vol. 31 ›› Issue (1): 154-172.

• 论文 • 上一篇    下一篇

含有一个控制的拟线性抛物系统的能控性

何红英|董旺远**   

  1. 华中农业大学理学院 武汉 430070
  • 收稿日期:2008-12-20 修回日期:2009-12-30 出版日期:2011-02-25 发布日期:2011-02-25
  • 基金资助:

    国家自然科学基金(60574017)和华中农业大学``薪火''专项(2009XH005)资助

Controllability of a Quasilinear System with One Control

 HE Hong-Ying, DONG Wang-Yuan**   

  1. College of Science, Huazhong Agricultural University, Wuhan 430070
  • Received:2008-12-20 Revised:2009-12-30 Online:2011-02-25 Published:2011-02-25
  • Supported by:

    国家自然科学基金(60574017)和华中农业大学``薪火''专项(2009XH005)资助

摘要:

该文讨论了一类拟线性抛物系统的全局零能控性和逼近能控性. 文中首先给出并证明了相应的线性系统的Carleman不等式,再由Carleman不等式去证明观测不等式, 最后利用Kakutani不动点定理证明非线性系统的全局零能控性和逼近能控性.

关键词: 零能控性, 逼近能控性, 拟线性系统

Abstract:

This work deals with a class of quasilinear systems and gives the global null controllability and approximate controllability. The key is to use an observability inequality for the linearized systems, which is established by a modified Carleman inequality obtained in this text and a fixed point theorem.

Key words: Null controllability, Approximate controllability, Quasilinear system

中图分类号: 

  • 93B05