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Journal Articles Discrete and Continuous Dynamical Systems - Series B Year : 2010

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

Abstract

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 \cite{linares-pazoto} 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.
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Dates and versions

hal-00453183 , version 1 (04-02-2010)

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Ademir F. Pazoto, Lionel Rosier. Uniform stabilization in weighted Sobolev spaces for the KdV equation posed on the half-line. Discrete and Continuous Dynamical Systems - Series B, 2010, 14 (4), pp.1511-1535. ⟨10.3934/dcdsb.2010.14.1511⟩. ⟨hal-00453183⟩
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