## Advances in Differential Equations

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

#### 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

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