Exact controllability of the nonlinear third-order dispersion equation

George, RK and Chalishajar, DN and Nandakumaran, AK (2007) Exact controllability of the nonlinear third-order dispersion equation. In: Journal of Mathematical Analysis and Applications, 332 (2). pp. 1028-1044.

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Abstract

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.

Item Type:	Journal Article
Publication:	Journal of Mathematical Analysis and Applications
Publisher:	Elsevier
Additional Information:	Copyright of this article belongs to Elsevier.
Keywords:	Korteweg–de Vries equation;Third-order dispersion equation;Monotone operator theory;Lipschitz continuity;Integral contractors
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	08 Aug 2007
Last Modified:	19 Sep 2010 04:38
URI:	http://eprints.iisc.ac.in/id/eprint/11667

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