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

 

Uniform stabilization of a nonlinear dispersive system


Authors: A. F. Pazoto and G. R. Souza
Journal: Quart. Appl. Math. 72 (2014), 193-208
MSC (2010): Primary 93D15, 93B05; Secondary 35B40, 35Q53
Published electronically: December 6, 2013
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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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Additional Information

A. F. Pazoto
Affiliation: Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21941-909, Rio de Janeiro, RJ, Brazil
Email: ademir@im.ufrj.br

G. R. Souza
Affiliation: Federal Center of Technology Education Celso Suckow da Fonseca, CEFET-RJ, Avenida Governador Roberto Silveira, 1900, CEP 28.635-000, Nova Friburgo, RJ, Brazil
Email: gilmar@im.ufrj.br

DOI: http://dx.doi.org/10.1090/S0033-569X-2013-01343-1
PII: S 0033-569X(2013)01343-1
Keywords: Exponential decay, stabilization, Korteweg-de Vries equation.
Received by editor(s): May 21, 2012
Published electronically: December 6, 2013
Additional Notes: The first author was partially supported by CNPq (Brazil).
The second author was partially supported by Capes (Brazil).
Article copyright: © Copyright 2013 Brown University



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