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CARLEMAN ESTIMATE AND UNIQUE CONTINUATION PROPERTY FOR THE LINEAR STOCHASTIC KORTEWEG–DE VRIES EQUATION

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

Published online by Cambridge University Press:  05 June 2014

PENG GAO
PENG GAO*
Affiliation:
Institute of Mathematics, Jilin University, Changchun 130012, PR China email gaopengjilindaxue@126.com
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Abstract

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In this paper, we obtain the well posedness of the linear stochastic Korteweg–de Vries equation by the Galerkin method, and then establish the Carleman estimate, leading to the unique continuation property (UCP) for the linear stochastic Korteweg–de Vries equation. This UCP cannot be obtained from the classical Holmgren uniqueness theorem.

Keywords

linear stochastic Korteweg–de Vries equationCarleman estimateunique continuation property

MSC classification

Secondary: 35Q53: KdV-like equations (Korteweg-de Vries) 60H15: Stochastic partial differential equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 2 , October 2014 , pp. 283 - 294
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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