Exact controllability of the nonlinear third-order dispersion equation

被引：30

作者：

George, R. K.

Chalishajar, D. N. ^{[1
]}

Nandakumaran, A. K.

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Gujarat Univ, Sardar Vallabhbhai Patel Inst Technol, Dept Appl Math, Vasad 388306, Gujarat, India

[3] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 332卷 / 02期

关键词：

Korteweg-de Vries equation; third-order dispersion equation; monotone operator theory; Lipschitz continuity; integral contractors;

D O I：

10.1016/j.jmaa.2006.10.084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Exact controllability of a nonlinear dispersion system has been studied. This work extends the work of Russell and Zhang [D.L. Russell, B.Y. Zhang, Controllability and stabilizability of the third-order linear dispersion equation on a periodic domain, SIAM J. Control Optim. 31 (1993) 659-676], in which the authors considered a linear dispersion system. We obtain controllability results using two standard types of nonlinearities, namely, Lipschitzian and monotone. We also obtain the exact controllability of the same system through the approach of Integral Contractors which is a weaker condition than Lipschitz condition. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1028 / 1044

页数：17

共 12 条

[1]

ALTMAN M, 1978, CONTRACTORS CONTRACT

[2] APPROXIMATE CONTROLLABILITY OF SEMILINEAR SYSTEMS USING INTEGRAL CONTRACTORS [J].