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A NEW UNIQUE CONTINUATION PROPERTY FOR THE KORTEWEG–DE VRIES EQUATION

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  10 January 2014

MO CHEN  and
PENG GAO
MO CHEN*
Affiliation:
Institute of Mathematics, Jilin University, Changchun 130012, PR China email [email protected]
PENG GAO
Affiliation:
Institute of Mathematics, Jilin University, Changchun 130012, PR China email [email protected]
*
✉[email protected]
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Abstract

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The aim of this paper is to obtain a new unique continuation property (UCP) for the Korteweg–de Vries equation posed on a finite interval. Compared with the previous UCP, we need fewer conditions on the solution. For this purpose, we have to establish a global Carleman estimate for the Korteweg–de Vries equation.

Keywords

Korteweg–de Vries equationunique continuation propertyCarleman estimate

MSC classification

Secondary: 35Q53: KdV-like equations (Korteweg-de Vries)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 90 - 98
Copyright
Copyright ©2014 Australian Mathematical Publishing Association Inc. 

References

Boussinesq, J., ‘Essai sur la théorie des eaux courantes’, Mémoires présentés par divers savants à l’Acad. des Sci. Inst. Nat. France 23 (1877), 1–680.Google Scholar
Glass, O. and Guerrero, S., ‘Some exact controllability results for the linear KdV equation and uniform controllability in the zero-dispersion limit’, Asymptot. Anal. 60 (2008), 61–100.Google Scholar
Korteweg, D. J. and de Vries, G., ‘On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves’, Philos. Mag. 39 (1895), 422–443.CrossRefGoogle Scholar
Meléndez, P. G., ‘Lipschitz stability in an inverse problem for the mian coefficient of a Kuramoto-Sivashinsky type equation’, J. Math. Anal. Appl. 408 (2013), 275–290.CrossRefGoogle Scholar
Rosier, L., ‘Control of the surface of a fluid by a wavemaker’, ESAIM Control Optim. Cal. Var. 10 (2004), 346–380.Google Scholar
Rosier, L. and Zhang, B. Y., ‘Global stabilization of the generalized Korteweg–de Vries equation posed on a finite domain’, SIAM J. Control Optim. 45 (2006), 927–956.Google Scholar
Saut, J. C. and Scheurer, B., ‘Unique continuation for some evolution equations’, J. Differential Equations 66 (1987), 118–139.CrossRefGoogle Scholar
Zhang, B. Y., ‘Unique continuation for the Korteweg–de Vries equation’, SIAM J. Math. Anal. 23 (1992), 55–71.CrossRefGoogle Scholar
Zhou, Z., ‘Observability estimate and null controllability for one-dimensional fourth order parabolic equation’, Taiwanese J. Math. 16 (2012), 1991–2017.Google Scholar