ON THE CONTROLLABILITY OF A COUPLED SYSTEM OF TWO KORTEWEG-DE VRIES EQUATIONS

被引：20

作者：

Micu, Sorin ^{[1
]}

Ortega, Jaime H. ^{[2
,3
]}

Pazoto, Ademir F. ^{[4
]}

机构：

[1] Univ Craiova, Fac Matemat Informat, Craiova 200585, Romania

[2] Univ Chile, Dept Ingn Matemat, UMI 2807, CNRS, Santiago, Chile

[3] Univ Chile, Ctr Modelamiento, UMI 2807, CNRS, Santiago, Chile

[4] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, Brazil

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2009年 / 11卷 / 05期

关键词：

Korteweg-de Vries equation and system; boundary control; observation; local controllability; EXACT BOUNDARY CONTROLLABILITY; STABILIZABILITY; STABILIZATION;

D O I：

10.1142/S0219199709003600

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proves the local exact boundary controllability property of a nonlinear system of two coupled Korteweg-de Vries equations which models the interactions of weakly nonlinear gravity waves (see [10]). Following the method in [24], which combines the analysis of the linearized system and the Banach's fixed point theorem, the controllability problem is reduced to prove a nonstandard unique continuation property of the eigenfunctions of the corresponding differential operator.

引用

页码：799 / 827

页数：29

共 50 条

[21] Numerical integration of a coupled Korteweg-de Vries system
Halim, AA
Kshevetskii, SP
Leble, SB
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (4-5) : 581 - 591
[22] Solitary waves of a coupled Korteweg-de Vries system
Grimshaw, R
Iooss, G
MATHEMATICS AND COMPUTERS IN SIMULATION, 2003, 62 (1-2) : 31 - 40
[23] Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces
Mo Chen
Mediterranean Journal of Mathematics, 2018, 15
[24] Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces
Chen, Mo
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (03)
[25] Boundary controllability of a Korteweg-de Vries-type Boussinesq system
Komornik, Vilmos
Pazoto, Ademir F.
Vieira, Miguel D. Soto
MATHEMATISCHE NACHRICHTEN, 2024, 297 (12) : 4478 - 4496
[26] Exact boundary controllability of the Korteweg-de Vries equation
Zhang, BY
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (02) : 543 - 565
[27] Complete integrability of two-coupled discrete modified Korteweg-de Vries equations
Sahadevan, R.
Balakrishnan, S.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (41)
[28] An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma-Coupled Korteweg-de Vries and Coupled Modified Korteweg-de Vries Equations
Veeresha, P.
Prakasha, D. G.
Kumar, Devendra
Baleanu, Dumitru
Singh, Jagdev
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2020, 15 (07):
[29] GLOBAL CONTROLLABILITY OF A NONLINEAR KORTEWEG-DE VRIES EQUATION
Chapouly, Marianne
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2009, 11 (03) : 495 - 521
[30] Exact boundary controllability for Korteweg-de Vries equation
Salem, Ali
INTELLIGENT SYSTEMS AND AUTOMATION, 2009, 1107 : 231 - 236

← 1 2 3 4 5 →