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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

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


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
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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Additional Information

C. P. Massarolo
Affiliation: Centro de Engenharias e Ciências Exatas, Universidade Estadual do Oeste do Paraná, Av. Tarquínio Joslin dos Santos, 1300, CEP 85870-650, Foz do Iguaçu, PR, Brazil
Email: claiton@unioeste.br

G. P. Menzala
Affiliation: National Laboratory of Scientific Computation, LNCC/MCT, Rua Getulio Vargas, 333, Quitandinha, Petrópolis, CEP 25651-070, RJ, Brasil and Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21945-970, Rio de Janeiro, RJ, Brasil
Email: perla@lncc.br

A. F. Pazoto
Affiliation: Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21945-970, Rio de Janeiro, RJ, Brasil
Email: ademir@im.ufrj.br

DOI: http://dx.doi.org/10.1090/S0033-569X-2011-01245-6
PII: S 0033-569X(2011)01245-6
Keywords: Exponential decay, stabilization, Korteweg-de Vries equation.
Received by editor(s): March 19, 2010
Published electronically: July 1, 2011
Additional Notes: CPM was supported by CNPq (Brazil) and MathAmsud.
GPM was supported by a Grant of CNPq, Proc. 301134/2009-0, PROSUL, Proc. 490329/2008-0 (Brazil) and MathAmsud. He acknowledges very much such important support.
AFP was supported by CNPq, PROSUL and MathAmsud.
Article copyright: © Copyright 2011 Brown University



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