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Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line

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  • Studied here is the large-time behavior of solutions of the Korteweg-de Vries equation posed on the right half-line under the effect of a localized damping. Assuming as in [19] that the damping is active on a set $(a_0,+\infty)$ with $a_0>0$, we establish the exponential decay of the solutions in the weighted spaces $L^2((x+1)^mdx)$ for $m\in $N* and $L^2(e^{2bx}dx)$ for $b>0$ by a Lyapunov approach. The decay of the spatial derivatives of the solution is also derived.
    Mathematics Subject Classification: Primary: 93D15, 35Q53; Secondary: 93C20.


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