Differential and Integral Equations

Global well-posedness of two initial-boundary-value problems for the Korteweg-de Vries equation

A. V. Faminskii

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Abstract

Two initial--boundary-value problems for the Korteweg--de~Vries equation in a half-strip with two boundary conditions and in a bounded rectangle are considered and results on local and global well-posedness of these problems are established in Sobolev spaces of various orders, including fractional. Initial and boundary data satisfy natural (or close to natural) conditions, originating from properties of solutions of a corresponding initial-value problem for a linearized KdV equation. An essential part of the study is the investigation of special solutions of a ``boundary potential" type for this linearized KdV equation.

Article information

Source
Differential Integral Equations Volume 20, Number 6 (2007), 601-642.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039428

Mathematical Reviews number (MathSciNet)
MR2319458

Zentralblatt MATH identifier
1212.35409

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Citation

Faminskii, A. V. Global well-posedness of two initial-boundary-value problems for the Korteweg-de Vries equation. Differential Integral Equations 20 (2007), no. 6, 601--642. https://projecteuclid.org/euclid.die/1356039428.


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