Uniform stabilization of a nonlinear dispersive system

Pazoto, A.; Souza, G.

doi:10.1090/S0033-569X-2013-01343-1

Authors: A. F. Pazoto and G. R. Souza
Journal: Quart. Appl. Math. 72 (2014), 193-208
MSC (2010): Primary 93D15, 93B05; Secondary 35B40, 35Q53.
DOI: https://doi.org/10.1090/S0033-569X-2013-01343-1
Published electronically: December 6, 2013
MathSciNet review: 3185138
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Abstract: The purpose of this work is to study the internal stabilization of a coupled system of two generalized Korteweg-de Vries equations under the effect of a localized damping term. To obtain the decay we use multiplier techniques combined with compactness arguments and reduce the problem to prove a unique continuation property for weak solutions. A locally exponential decay result is derived.

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