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On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping
Author(s):
F.
Linares;
A.
F.
Pazoto
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1515-1522.
MSC (2000):
Primary 93D15, 93B05, 35Q53
Posted:
January 9, 2007
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Abstract:
This paper is concerned with the asymptotic behavior of solutions of the critical generalized Korteweg-de Vries equation in a bounded interval with a localized damping term. Combining multiplier techniques and compactness arguments it is shown that the problem of exponential decay of the energy is reduced to prove the unique continuation property of weak solutions. A locally uniform stabilization result is derived.
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Additional Information:
F.
Linares
Affiliation:
IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460--320, Brazil
Email:
linares@impa.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@acd.ufrj.br
DOI:
10.1090/S0002-9939-07-08810-7
PII:
S 0002-9939(07)08810-7
Keywords:
Exponential decay,
stabilization,
Korteweg-de Vries equation
Received by editor(s):
October 24, 2005
Received by editor(s) in revised form:
February 24, 2006
Posted:
January 9, 2007
Additional Notes:
The first author was partially supported by CNPq, Brazil
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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