数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1593-1604.doi: 10.1016/S0252-9602(10)60152-X

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CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT

许友军1|刘振海2   

  1. 1.School of Mathematics and Physics, University of South China, |Hengyang |421001, China;
    2.School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China
  • 收稿日期:2008-03-19 修回日期:2009-01-15 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    The authors were supported financially by the National Natural Science Foundation of China (10971019), The author (Y. Xu) was supported financially by the Scientific Research Fund of Hunan Provincial Educational Department (09C852).

CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT

 XU You-Jun1, LIU Zhen-Hai2   

  1. 1.School of Mathematics and Physics, University of South China, |Hengyang |421001, China;
    2.School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China
  • Received:2008-03-19 Revised:2009-01-15 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    The authors were supported financially by the National Natural Science Foundation of China (10971019), The author (Y. Xu) was supported financially by the Scientific Research Fund of Hunan Provincial Educational Department (09C852).

摘要:

In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN. The results are established by using the variational methods, the related duality theory and Kakutani
Fixed-point Theorem.

关键词: controllability, Kakutani fixed-point theorem, nonlinear gradient term

Abstract:

In this article, we consider the controllability of a quasi-linear heat equation involving gradient terms with Dirichlet boundary conditions in a bounded domain of RN. The results are established by using the variational methods, the related duality theory and Kakutani
Fixed-point Theorem.

Key words: controllability, Kakutani fixed-point theorem, nonlinear gradient term

中图分类号: 

  • 35K55