Uniform stabilization of a class of coupled systems of KdV equations with localized damping

Massarolo, C.; Menzala, G.; Pazoto, A.

doi:10.1090/S0033-569X-2011-01245-6

Authors: C. P. Massarolo, G. P. Menzala and A. F. Pazoto
Journal: Quart. Appl. Math. 69 (2011), 723-746
MSC (2000): Primary 93D15, 93B05; Secondary 35B40, 35Q53.
DOI: https://doi.org/10.1090/S0033-569X-2011-01245-6
Published electronically: July 1, 2011
MathSciNet review: 2893997
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Abstract: We study the stabilization of solutions of a coupled system of Korteweg-de Vries (KdV) equations in a bounded interval under the effect of a localized damping term. We use multiplier techniques combined with the so-called “compactness-uniqueness argument”. The problem is then reduced to proving a unique continuation property (UCP) for weak solutions. The exponential decay of solutions was previously obtained in Bisognin, Bisognin, and Menzala (2003) when the damping was effective simultaneously in neighborhoods of both extremes of the bounded interval. In this work we address the general case using a different approach to obtain the UCP and stabilize the system.

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