Null controllability and numerical method for Crocco equation with incomplete data based on an exponential integrator and finite difference-finite element method

We consider the linearized Crocco equation in fluid dynamics with incomplete data and Robin boundary conditions, and address theoretical and numerical distributed null control. The controllability problem is solved through a dual reformulation. We first resolve some constrained extremal problems and apply appropriated duality techniques that lead to the formulation of equivalent unconstrained extremal problem in variational form. Novel numerical technique based on finite difference-finite element space discretization and exponential integrator in time discretization is proposed. For illustration, numerical simulations are provided.