This Python module approximates the solution of an optimal control problem for the two-dimensional steady Boussinesq equation with regular Borel measures as controls. The problem being considered is the following:
min (1/2)|u - ud|^2 + (1/2)|z - zd|^2 + a|q| + b|y|
subject to the state equation:
- nu Delta u + (u.Grad) u + Grad p = zg + q in Omega
div u = 0 in Omega
- kappa Delta z + (u.Grad) z = y in Omega
u = 0 on Gamma
z = 0 on Gamma
over all controls q in M(Omega) x M(Omega) and y in M(Omega).
If you find these codes useful, you can cite the manuscript as:
Peralta, G., Optimal Borel measure controls for the two-dimensional stationary Boussinesq system, to appear in ESAIM: Control, Optimisation and Calculus of Variations, 2022.