scholarly journals Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Exequiel Mallea-Zepeda ◽  
Eber Lenes ◽  
Elvis Valero
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Mixed Boundary Conditions ◽  
Slip Boundary Condition ◽  
Heat Convection ◽  
Existence Of Optimal Solutions ◽  
Slip Boundary ◽  
Boundary Control Problem

We analyze an optimal boundary control problem for heat convection equations in a three-dimensional domain, with mixed boundary conditions. We prove the existence of optimal solutions, by considering boundary controls for the velocity vector and the temperature. The analyzed optimal control problem includes the minimization of a Lebesgue norm between the velocity and some desired field, as well as the temperature and some desired temperature. By using the Lagrange multipliers theorem we derive an optimality system. We also give a second-order sufficient condition.

Numerical Investigation of the Drag and Lift Forces Acting on Impenetrable Rotating Spherical Nano-Particle

2008 ◽  
Author(s):  
M. R. Meigounpoory ◽  
A. Rahi ◽  
A. Mirbozorgi
Keyword(s):  
Lift Coefficient ◽  
Three Dimensional ◽  
Slip Boundary Condition ◽  
Slip Condition ◽  
Nano Particle ◽  
Slip Coefficient ◽  
Slip Boundary ◽  
Lift Forces ◽  
Drag And Lift ◽  
Drag And Lift Coefficient

The drag and lift forces acting on a rotating impenetrable spherical suspended nano-particle in a homogeneous uniform flow are numerically studied by means of a three-dimensional numerical simulation with slip boundary condition. The effects of both the slip coefficient and rotational speed of the nanosphere on the drag and lift forces are investigated for Reynolds numbers in the range of 0.1 < Re < 100. Increase of rotation increases the drag and lift force exerted by flow at the surface of nano-sphere. By increasing slip coefficient the values of drag and lift coefficients decreases. At full slip condition, rotation of the nano-sphere has not significant effects on the drag and lift coefficient values moreover the lift coefficient of flow around the rotating spherical particle will be vanished. Present numerical results at no-slip condition are in good agreements with certain results of flow around of rotating sphere.

scholarly journals BOUNDARY CONTROL PROBLEM FOR ONE DEGENERATE HIBERBOLIC EQUATION

2019 ◽  
pp. 19-27
Author(s):  
А.Х. Аттаев
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Sufficient Conditions ◽  
Analytical Form ◽  
Cauchy Data ◽  
Boundary Control Problem ◽  
Order Hyperbolic Equation ◽  
Boundary Controls ◽  
Necessary And Sufficient ◽  
Second Order Hyperbolic Equation

В работе изучается задача граничного управления для вырождающегося гиперболического уравнения второго порядка. Установлены необходимые и достаточные условия управляемости данными Коши за минимальный промежуток времени. Граничные управления предъявлены в явном аналитическом виде. The paper studies the boundary control problem for a degenerate second-order hyperbolic equation. Necessary and sufficient conditions are established for minimal time controllability over Cauchy data. Boundary controls are presented in an explicit analytical form.

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