WELL-POSEDNESS OF A CLASS OF NON-HOMOGENEOUS BOUNDARY VALUE PROBLEMS OF THE KORTEWEG-DE VRIES EQUATION ON A FINITE DOMAIN

被引：16

作者：

Kramer, Eugene ^{[1
]}

Rivas, Ivonne ^{[2
,3
]}

Zhang, Bing-Yu ^{[2
]}

机构：

[1] Univ Cincinnati, Raymond Walters Coll, Dept Math Phys & Comp Sci, Cincinnati, OH 45236 USA

[2] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

[3] IMPA, BR-22460320 Rio De Janeiro, Brazil

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 02期

关键词：

The Kortweg-de Vries equation; well-posedness; non-homogeneous boundary value problem; GENERALIZED KORTEWEG; DEVRIES EQUATION; QUARTER-PLANE; CONTROLLABILITY; STABILIZATION; KDV; RESPECT; DECAY;

D O I：

10.1051/cocv/2012012

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0, L). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space H-s (0, L) for s > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [Adv. Differ. Equ. 6 (2001) 1463-1492].

引用

页码：358 / 384

页数：27

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