Advances in Differential Equations

Lower regularity solutions of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

Chaohua Jia, Ivonne Rivas, and Bing-Yu Zhang

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Abstract

In this paper, we study an initial-boundary value problem of the Korteweg-de Vries equation posed on a bounded interval $(0,L)$ with nonhomogeneous boundary conditions, which is known to be locally well-posed in the Sobolev space $H^s(0,L)$ with $s\gt-3/4$. Taking the advantage of the hidden dissipative mechanism and the sharp trace regularities of its solutions, we show that the problem is locally well-posed in the space $H^s(0,L)$ with $s\gt-1$.

Article information

Source
Adv. Differential Equations Volume 19, Number 5/6 (2014), 559-584.

Dates
First available in Project Euclid: 3 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1396558061

Mathematical Reviews number (MathSciNet)
MR3189094

Zentralblatt MATH identifier
1291.35289

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35Q35: PDEs in connection with fluid mechanics

Citation

Jia, Chaohua; Rivas, Ivonne; Zhang, Bing-Yu. Lower regularity solutions of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain. Adv. Differential Equations 19 (2014), no. 5/6, 559--584. https://projecteuclid.org/euclid.ade/1396558061.


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