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].
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页码：358 / 384
页数：27
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