Abstract: In this paper, we prove the unique continuation property (UPC) and decay about the Korteweg-deBurgers (KdVB) equation in a bounded interval with a localized damping term. We will show that the UPC holds with the condition of u x (0, t) = 0 and u ≡ 0 in ω × (0, T ), where ω is a nonempty open subset of (0, L), if a localized damping acting on a moving internal is applied in KdVB equation. And we prove the exponential decay of the KdVB equation with some boundary and initial condition
