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On the uniform decay for the Korteweg–de Vries equation with weak damping

✍ Scribed by C. P. Massarolo; G. P. Menzala; A. F. Pazoto

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
170 KB
Volume
30
Category
Article
ISSN
0170-4214

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✦ Synopsis

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.

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On the Stochastic Korteweg–de Vries Equa
On the Stochastic Korteweg–de Vries Equation
✍ A de Bouard; A Debussche 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 429 KB

We consider a stochastic Korteweg de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions in H 1 (R) in the case of additive noise and existence of martingales solution