Bang-bang optimal control problems for the viscous Camassa-Holm equations

被引：0

作者：

Anh, Cung The ^{[1
]}

Giang, Nguyen Hai Ha ^{[1
]}

Son, Vu Hai ^{[1
]}

机构：

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

来源：

OPTIMIZATION | 2025年

关键词：

Navier-Stokes equation; 3D viscous Camassa-Holm equations; optimal control; bang-bang control; sufficient optimality conditions; stability analysis; Tikhonov term; SUFFICIENT 2ND-ORDER CONDITIONS; VELOCITY TRACKING PROBLEM; NAVIER-STOKES EQUATIONS; DATA ASSIMILATION; NULL CONTROLLABILITY; STABILITY ANALYSIS; EXISTENCE; DECAY; ATTRACTORS;

D O I：

10.1080/02331934.2025.2494260

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：

We study optimal control problems for three-dimensional viscous Camassa-Holm equations in bounded domains with convex control constraints and a quadratic cost functional which does not involve the quadratic term for the control. We show the existence of optimal solutions, necessary optimality conditions and sufficient optimality condition. Furthermore, we also establish stability results for optimal solutions with respect to the regularizing Tikhonov term.

引用

页数：29

共 52 条

[1]

Abergel F., 1990, Theoretical Computational Fluid Dynamics, V1, P303, DOI [DOI 10.1007/BF00271794, 10.1007/bf00271794]

[2] Continuous data assimilation for the three-dimensional Navier-Stokes-α model [J].

Albanez, Debora A. F. ;

Nussenzveig Lopes, Helena J. ;

Titi, Edriss S. .

ASYMPTOTIC ANALYSIS, 2016, 97 (1-2) :139-164

[3] Pontryagin's principle and variational inequality for optimal control problems governed by viscous Camassa-Holm equations [J].

Anh, Cung The ;

Ha Giang, Nguyen Hai ;

Nguyen, Than Thi Thuy .

OPTIMIZATION, 2024, 73 (13) :3899-3926

[4]

Aubin J.-P., 1990, SET-VALUED ANAL, DOI 10.1007/978-0-8176-4848-0

[5] SECOND ORDER ANALYSIS FOR STRONG SOLUTIONS IN THE OPTIMAL CONTROL OF PARABOLIC EQUATIONS [J].

Bayen, Terence ;

Silva, Francisco J. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (02) :819-844

[6]

Bayen T, 2014, T AM MATH SOC, V366, P2063

[7] On questions of decay and existence for the viscous Camassa-Holm equations [J].

Bjorland, Clayton ;

Schonbek, Maria E. .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (05) :907-936

[8] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[9]

Casas E., 2015, Jahresber. Dtsch.Math.-Ver, P3, DOI DOI 10.1365/S13291-014-0109-3

[10] NEW ASSUMPTIONS FOR STABILITY ANALYSIS IN ELLIPTIC OPTIMAL CONTROL PROBLEMS [J].

Casas, Eduardo ;

Corella, Alberto Dominguez ;

Jork, Nicolai .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2023, 61 (03) :1394-1414

← 1 2 3 4 5 6 →