Boundary value and extremum problems for generalized Oberbeck–Boussinesq model

Boundary value and extremum problems for a generalized Oberbeck–Boussinesq model are considered under the assumption that the reaction coefficient depends nonlinearly on the substance's concentration. In the case when reaction coefficient and cost functionals are Fréchet differentiable, an optimality system for the extremum problem is obtained. For the quadratic reaction coefficient a local uniqueness of the optimal solution is proved.