Optimality Conditions for Boundary Control Problems of Parabolic Type

1994 ◽  
pp. 79-96 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Maria Elisabetta Tessitore
Keyword(s):  
Optimality Conditions ◽  
Boundary Control ◽  
Parabolic Type ◽  
Control Problems ◽  
Boundary Control Problems

Optimal boundary control for the stationary Boussinesq equations with variable density

2019 ◽  
Vol 22 (05) ◽  
pp. 1950031
Author(s):  
José Luiz Boldrini ◽  
Exequiel Mallea-Zepeda ◽  
Marko Antonio Rojas-Medar
Keyword(s):  
Boundary Conditions ◽  
Optimality Conditions ◽  
Boundary Control ◽  
Boussinesq Equations ◽  
Variable Density ◽  
Control Problems ◽  
Dynamical Equations ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
Boundary Control Problems

Certain classes of optimal boundary control problems for the Boussinesq equations with variable density are studied. Controls for the velocity vector and temperature are applied on parts of the boundary of the domain, while Dirichlet and Navier friction boundary conditions for the velocity and Dirichlet and Robin boundary conditions for the temperature are assumed on the remaining parts of the boundary. As a first step, we prove a result on the existence of weak solution of the dynamical equations; this is done by first expressing the fluid density in terms of the stream-function. Then, the boundary optimal control problems are analyzed, and the existence of optimal solutions are proved; their corresponding characterization in terms of the first-order optimality conditions are obtained. Such optimality conditions are rigorously derived by using a penalty argument since the weak solutions are not necessarily unique neither isolated, and so standard methods cannot be applied.

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