First-order necessary conditions of optimality for the optimal control of two-dimensional convective Brinkman–Forchheimer equations with state constraints. (9th December 2022) - Mohan, Manil T.
Abstract : This work is concerned about some distributed optimal control problems governed by two-dimensional convective Brinkman–Forchheimer (CBF) equations, which describe the motion of incompressible viscous fluid through a rigid, homogeneous, isotropic, porous medium. We address a distributed optimal control problem of minimizing a suitable cost functional subjected to 2D CBF equations with state constraints. We establish the existence of an optimal solution and obtain the first-order necessary conditions of optimality for such optimal control problems.