Optimal Boundary Control of Non-Isothermal Viscous Fluid Flow

被引：28

作者：

Baranovskii, Evgenii S. ^{[1
]}

Domnich, Anastasia A. ^{[1
]}

Artemov, Mikhail A. ^{[1
]}

机构：

[1] Voronezh State Univ, Dept Appl Math Informat & Mech, Voronezh 394018, Russia

来源：

FLUIDS | 2019年 / 4卷 / 03期

关键词：

non-isothermal flows; creeping flows; viscous fluid; optimal control; boundary control; pressure boundary conditions; weak solution; existence theorem; marginal function; EXACT CONTROLLABILITY; BOUSSINESQ; HEAT; SOLVABILITY;

D O I：

10.3390/fluids4030133

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We study an optimal control problem for the mathematical model that describes steady non-isothermal creeping flows of an incompressible fluid through a locally Lipschitz bounded domain. The control parameters are the pressure and the temperature on the in-flow and out-flow parts of the boundary of the flow domain. We propose the weak formulation of the problem and prove the existence of weak solutions that minimize a given cost functional. It is also shown that the marginal function of this control system is lower semi-continuous.

引用

页数：14

共 20 条

[1]

Alekseev GV, 2010, ADV MATH FLUID MECH, P1

[2] Stability of Optimal Controls for the Stationary Boussinesq Equations [J].

Alekseev, Gennady ;

Tereshko, Dmitry .

INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 2011

[3] Solvability of stationary boundary control problems for heat convection equations [J].

Alekseev, GV .

SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (05) :844-858

[4] Solvability of inverse extremal problems for stationary heat and mass transfer equations [J].

Alekseev, GV .

SIBERIAN MATHEMATICAL JOURNAL, 2001, 42 (05) :811-827

[5]

[Anonymous], 2007, CONTROL COUPLED PART

[6]

Conca C., 1994, Japan. J. Math. (N.S.), V20, P279, DOI DOI 10.4099/MATH1924.20.279

[7]

Fursikov A.V., 2000, Optimal Control of Distributed Systems: Theory and Applications

[8] Exact controllability of the Navier-Stokes and Boussinesq equations [J].

Fursikov, AV ;

Imanuvilov, OY .

RUSSIAN MATHEMATICAL SURVEYS, 1999, 54 (03) :565-618

[9] Local exact controllability to the trajectories of the Boussinesq system [J].

Guerrero, S .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (01) :29-61

[10] Optimal boundary control of a system describing thermal convection [J].

Korotkii, A. I. ;

Kovtunov, D. A. .

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2011, 272 :74-100

← 1 2 →