An optimal control problem of the 3D viscous Camassa-Holm equations

被引：3

作者：

Cung The Anh ^{[1
]}

Dang Thanh Son ^{[2
]}

机构：

[1] Hanoi Natl Univ Educ, Dept Math, Hanoi, Vietnam

[2] Telecommun Univ, Fdn Sci Fac, Nha Trang, Khanh Hoa, Vietnam

来源：

OPTIMIZATION | 2021年 / 70卷 / 01期

关键词：

viscous Camassa-Holm equations; optimal control; existence; necessary optimality condition; sufficient optimality condition; NAVIER-STOKES EQUATIONS; GLOBAL WELL-POSEDNESS; DATA ASSIMILATION; EXISTENCE; DECAY;

D O I：

10.1080/02331934.2019.1696340

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we study an optimal control problem of the three-dimensional viscous Camassa-Holm equations in bounded domains with Dirichlet boundary conditions and a quadratic objective functional. We first prove the existence of an optimal solution. Then we establish the first-order necessary and second-order sufficient optimality conditions.

引用

页码：3 / 25

页数：23

共 50 条

[31] The existence of solution for viscous Camassa-Holm equations on bounded domain in five dimensions
Yu, Yongjiang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 429 (02) : 849 - 872
[32] On the Cauchy problem of the Camassa-Holm equation
Dai H.-H.
Kwek K.-H.
Gao H.-J.
Qu C.-C.
Frontiers of Mathematics in China, 2006, 1 (1) : 144 - 159
[33] On the scattering problem for the Camassa-Holm equation
Constantin, A
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2008): : 953 - 970
[34] THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS
杨灵娥
纪艳珊
郭柏灵
Acta Mathematica Scientia, 2009, 29 (01) : 65 - 73
[35] THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS
Yang Linge
Ji Yanshan
Guo Boling
ACTA MATHEMATICA SCIENTIA, 2009, 29 (01) : 65 - 73
[36] Local null controllability of viscous Camassa-Holm equation
Mitra, Debanjana
JOURNAL OF EVOLUTION EQUATIONS, 2018, 18 (02) : 627 - 657
[37] On the Camassa-Holm and Hunter-Saxton equations
Holden, H
European Congress of Mathematics, 2005, : 173 - 200
[38] Derivation of the Camassa-Holm equations for elastic waves
Erbay, H. A.
Erbay, S.
Erkip, A.
PHYSICS LETTERS A, 2015, 379 (12-13) : 956 - 961
[39] Global wellposedness of cubic Camassa-Holm equations
Zhang, Qingtian
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 133 : 61 - 73
[40] Time periodic solution of the viscous Camassa-Holm equation
Fu, YP
Guo, BL
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 313 (01) : 311 - 321

← 1 2 3 4 5 →