Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain

被引：20
作者：
Kramer, Eugene F. [1 ]
Zhang, Bingyu [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
来源：
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2010年 / 23卷 / 03期
关键词：
KdV equation; Korteweg-de Vries equation; well-posed; DEVRIES EQUATION; GENERALIZED KORTEWEG; WELL-POSEDNESS; PERIODIC DOMAIN; KDV; CONTROLLABILITY; STABILIZATION; GENERATION; REGULARITY; INTEGRALS;
D O I：
10.1007/s11424-010-0143-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space H (s) (0, 1) for any s a parts per thousand yen 0 via the contraction mapping principle.
引用
收藏
页码：499 / 526
页数：28
相关论文
共 74 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]   THE KORTEWEG-DEVRIES EQUATION, POSED IN A QUARTER-PLANE [J].
BONA, J ;
WINTHER, R .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1983, 14 (06) :1056-1106
[3]   SOLUTIONS OF KORTEWEG-DEVRIES EQUATION IN FRACTIONAL ORDER SOBOLEV SPACES [J].
BONA, J ;
SCOTT, R .
DUKE MATHEMATICAL JOURNAL, 1976, 43 (01) :87-99
[4]  
Bona J.L., 1999, CONTEMP MATH, V221, P59, DOI DOI 10.1090/CONM/221/03118
[5]  
Bona JL, 2006, DYNAM PART DIFFER EQ, V3, P1
[6]  
Bona JL, 2004, ADV DIFFERENTIAL EQU, V9, P241
[7]   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
[8]   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
[9]   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
[10]   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
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