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

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

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