Abstract
This paper is devoted to studying the 1-D viscous Camassa-Holm equation on a bounded interval. We first deduce the existence and uniqueness of strong solution to the viscous Camassa-Holm equation by using Galerkin method. Then we establish an identity for a second order parabolic operator, by applying this identity we obtain two global Carleman estimates for the linear viscous Camassa-Holm operator. Based on these estimates, we obtain two types of Unique Continuation Property for the viscous Camassa-Holm equation.
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