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

共 50 条

[1] LOWER REGULARITY SOLUTIONS OF A CLASS OF NON-HOMOGENEOUS BOUNDARY VALUE PROBLEMS OF THE KORTEWEG-DE VRIES EQUATION ON A FINITE DOMAIN
Jia, Chaohua
Rivas, Ivonne
Zhang, Bing-Yu
ADVANCES IN DIFFERENTIAL EQUATIONS, 2014, 19 (5-6) : 559 - 584
[2] Well-posedness of a nonlinear boundary value problem for the Korteweg-de Vries equation on a bounded domain
Caicedo, Miguel Andres
Zhang, Bing-Yu
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 448 (02) : 797 - 814
[3] WELL-POSEDNESS OF KORTEWEG-DE VRIES-BURGERS EQUATION ON A FINITE DOMAIN
Li, Jie
Liu, Kangsheng
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2017, 48 (01): : 91 - 116
[4] Well-posedness of Korteweg-de Vries-Burgers equation on a finite domain
Jie Li
Kangsheng Liu
Indian Journal of Pure and Applied Mathematics, 2017, 48 : 91 - 116
[5] GLOBAL WELL-POSEDNESS AND ASYMPTOTIC BEHAVIOR OF A CLASS OF INITIAL-BOUNDARY-VALUE PROBLEM OF THE KORTEWEG-DE VRIES EQUATION ON A FINITE DOMAIN
Rivas, Ivonne
Usman, Muhammad
Zhang, Bing-Yu
MATHEMATICAL CONTROL AND RELATED FIELDS, 2011, 1 (01) : 61 - 81
[6] A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain II
Bona, Jerry L.
Sun, Shu Ming
Zhang, Bing-Yu
JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 247 (09) : 2558 - 2596
[7] GLOBAL WELL-POSEDNESS OF TWO INITIAL-BOUNDARY-VALUE PROBLEMS FOR THE KORTEWEG-DE VRIES EQUATION
Faminskii, A. V.
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2007, 20 (06) : 601 - 642
[8] Rapid Boundary Stabilization of the Korteweg-de Vries Equation on a Bounded Domain I: Well-posedness
Wang Chengqiang
2013 32ND CHINESE CONTROL CONFERENCE (CCC), 2013, : 1316 - 1319
[9] Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane
Bona, Jerry L.
Sun, S. M.
Zhang, Bing-Yu
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (06): : 1145 - 1185
[10] Well-posedness of Korteweg-de Vries-Benjamin Bona Mahony equation on a finite domain
Li, Jie
Liu, Kangsheng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 452 (01) : 611 - 633

← 1 2 3 4 5 →