On the Rayleigh-Bénard-Marangoni system and a related optimal control problem
The paper under review considers an optimal control problem governed by the stationary Rayleigh-Benard-Marangoni system in 3D. Specifically, the controls act as the Dirichlet boundary condition of the Navier-Stokes equation on part of the boundary, and as the Dirichlet and Neumann boundary conditions of the heat equation. The authors study the well-posedness of the state equation as well as that of the optimal control problem. First order necessary optimality system is derived with the Lagrange multiplier theory, moreover, the authors derive the second order sufficient optimality condition.
scientific article; zbMATH DE number 6934578
scientific article