Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Stabilization of the Korteweg-de Vries equation with localized damping


Authors: G. Perla Menzala, C. F. Vasconcellos and E. Zuazua
Journal: Quart. Appl. Math. 60 (2002), 111-129
MSC: Primary 35Q53; Secondary 35B35, 35B40
DOI: https://doi.org/10.1090/qam/1878262
MathSciNet review: MR1878262
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Abstract: We study the stabilization of solutions of the Korteweg-de Vries (KdV) equation in a bounded interval under the effect of a localized damping mechanism. Using multiplier techniques we deduce the exponential decay in time of the solutions of the underlying linear equation. A locally uniform stabilization result of the solutions of the nonlinear KdV model is also proved. The proof combines compactness arguments, the smoothing effect of the KdV equation on the line and unique continuation results.


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DOI: https://doi.org/10.1090/qam/1878262
Article copyright: © Copyright 2002 American Mathematical Society


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