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
✦ LIBER ✦
On the Structure of the Two-Soliton Interaction for the Korteweg–de Vries Equation
✍ Scribed by Mikhail Kovalyov
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 123 KB
- Volume
- 152
- Category
- Article
- ISSN
- 0022-0396
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## 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
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