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On the uniform decay for the Korteweg–de Vries equation with weak damping |
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| Authors: | C. P. Massarolo G. P. Menzala A. F. Pazoto |
| Affiliation: | 1. Centro de Engenharias e Ciências Exatas, Universidade Estadual do Oeste do Paraná, Av. Tarquínio Joslin dos Santos, 1300, CEP 85870‐650, Foz do Igua?u, PR, Brazil;2. National Laboratory of Scientific Computation, LNCC/MCT, Rua Getulio Vargas, 333, Quitandinha, Petrópolis, CEP 25651‐070, RJ, Brazil;3. Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21945‐970, Rio de Janeiro, RJ, Brazil;4. Institute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21945‐970, Rio de Janeiro, RJ, BrazilInstitute of Mathematics, Federal University of Rio de Janeiro, UFRJ, P.O. Box 68530, CEP 21945‐970, Rio de Janeiro, RJ, Brazil=== |
| Abstract: | The aim of this work is to consider the Korteweg–de Vries equation in a finite interval with a very weak localized dissipation namely the H?1‐norm. Our main result says that the total energy decays locally uniform at an exponential rate. Our analysis improves earlier works on the subject (Q. Appl. Math. 2002; LX (1):111–129; ESAIM Control Optim. Calculus Variations 2005; 11 (3):473–486) and gives a satisfactory answer to a problem suggested in (Q. Appl. Math. 2002; LX (1):111–129). Copyright © 2007 John Wiley & Sons, Ltd. |
| Keywords: | exponential decay stabilization Korteweg– de Vries equation |