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

doi:10.1016/S0252-9602(10)60152-X

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

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

许友军¹|刘振海²

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.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/Abstract

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 R^N. 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:

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

中图分类号:

35K55

许友军, 刘振海. CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT[J]. 数学物理学报(英文版), 2010, 30(5): 1593-1604.

XU You-Jun, LIU Zhen-Hai. CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT[J]. Acta mathematica scientia,Series B, 2010, 30(5): 1593-1604.

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

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

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