On Existence of Optimal Solutions to Boundary Control Problem for an Elastic Body with Quasistatic Evolution of Damage

2013 ◽  
pp. 265-286 ◽  
Author(s):  
Peter I. Kogut ◽  
Günter Leugering
Keyword(s):  
Control Problem ◽  
Elastic Body ◽  
Boundary Control ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
Quasistatic Evolution ◽  
Boundary Control Problem

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.

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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