Advances in Differential Equations

An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval

Thierry Colin and Jean-Michel Ghidaglia

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The Korteweg--de Vries equation occurs as a model for unidirectional propagation of small amplitude long waves in numerous physical systems. The aim of this work is to propose a well-posed mixed initial--boundary value problem when the spacial domain is of finite extent. More precisely, we establish local existence of solutions for arbitrary initial data in the Sobolev space $H^1$ and global existence for small initial data in this space. In a second step we show global strong regularizing effects.

Article information

Source
Adv. Differential Equations Volume 6, Number 12 (2001), 1463-1492.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357139955

Mathematical Reviews number (MathSciNet)
MR1858429

Zentralblatt MATH identifier
1022.35055

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35A07

Citation

Colin, Thierry; Ghidaglia, Jean-Michel. An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval. Adv. Differential Equations 6 (2001), no. 12, 1463--1492. https://projecteuclid.org/euclid.ade/1357139955.


Export citation