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
收藏
页码：358 / 384
页数：27
相关论文
共 52 条
[1]   MODEL EQUATIONS FOR LONG WAVES IN NONLINEAR DISPERSIVE SYSTEMS [J].
BENJAMIN, TB ;
BONA, JL ;
MAHONY, JJ .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 272 (1220) :47-+
[2]  
Bona JL, 2006, DYNAM PART DIFFER EQ, V3, P1
[3]  
Bona JL, 2004, ADV DIFFERENTIAL EQU, V9, P241
[4]   Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane [J].
Bona, Jerry L. ;
Sun, S. M. ;
Zhang, Bing-Yu .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (06) :1145-1185
[5]   A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain II [J].
Bona, Jerry L. ;
Sun, Shu Ming ;
Zhang, Bing-Yu .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 247 (09) :2558-2596
[6]   A nonhomogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain [J].
Bona, JL ;
Sun, SM ;
Zhang, BY .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2003, 28 (7-8) :1391-1436
[7]   AN EVALUATION OF A MODEL EQUATION FOR WATER-WAVES [J].
BONA, JL ;
PRITCHARD, WG ;
SCOTT, LR .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1981, 302 (1471) :457-510
[8]   A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane [J].
Bona, JL ;
Sun, SM ;
Zhang, BY .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (02) :427-490
[9]   Forced oscillations of a damped Korteweg-De Vries equation in a quarter plane [J].
Bona, JL ;
Sun, SM ;
Zhang, BY .
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2003, 5 (03) :369-400
[10]  
Bourgain J., 1993, Geom. Funct. Anal., V3, P107
123456