Time Optimal Control Problem of the 2D MHD Equations with Memory

被引：2

作者：

Son, Dang Thanh ^{[1
]}

Toan, Nguyen Duong ^{[2
]}

机构：

[1] Telecommun Univ, Fdn Sci Fac, 101 Mai Xuan Thuong, Nha Trang, Vietnam

[2] Haiphong Univ, Fac Math & Nat Sci, 171 Phan Dang Luu, Haiphong, Vietnam

来源：

JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS | 2023年 / 29卷 / 04期

关键词：

2D MHD equations with memory; Time optimal control; Necessary optimality conditions; Sufficient optimality conditions; HEAT-EQUATION; VISCOELASTIC EQUATIONS; ASYMPTOTIC-BEHAVIOR; GLOBAL ATTRACTORS; EXISTENCE; STATIONARY; REGULARITY; UNIQUENESS; STABILITY; DENSITY;

D O I：

10.1007/s10883-022-09635-9

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 an optimal control problem for the 2D MHD equations with memory in bounded domains with Dirichlet boundary conditions, where the time needed to reach the desired state plays an essential role. We first prove the existence of optimal solutions. Then we establish the first-order necessary and second-order sufficient optimality conditions. The second-order optimality ones obtained in the paper seem to be optimal in the sense that the gap between them is minimal.

引用

页码：1323 / 1355

页数：33

共 57 条

[1] Non-uniform decay of MHD equations with and without magnetic diffusion [J].

Agapito, Ruben ;

Schonbek, Maria .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (10-12) :1791-1812

[2]

[Anonymous], 2010, Graduate Studies in Mathematics

[3]

Arada N, 2003, DISCRETE CONT DYN-A, V9, P1549

[4]

Aubin J.P., 1990, Set-valued analysis, DOI 10.1007/978-0-8176-4848-0

[5] The time optimal control of Navier-Stokes equations [J].

Barbu, V .

SYSTEMS & CONTROL LETTERS, 1997, 30 (2-3) :93-100

[6] A Distributed Control Approach for the Boundary Optimal Control of the Steady MHD Equations [J].

Bornia, G. ;

Gunzburger, M. ;

Manservisi, S. .

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 14 (03) :722-752

[7] Two regularity criteria for the 3D MHD equations [J].

Cao, Chongsheng ;

Wu, Jiahong .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (09) :2263-2274

[8]

Caraballo T, 2007, DISCRETE CONT DYN-A, V18, P253

[9]

Carlier G, 2010, J CONVEX ANAL, V17, P1007

[10] On some optimal control problems governed by a state equation with memory [J].

Carlier, Guillaume ;

Tahraoui, Rabah .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2008, 14 (04) :725-743

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