State and observer-based feedback control of normal flow equations

We investigate wellposedness and stability of normal flow equations with two different control schemes. The first one considers the velocity field as a control action and relies on a proportional regulator that is proved to be stable. In the second one, control acts on the source term and is based on an observer providing an estimate of the gradient of the normal flow solution; convergence properties are demonstrated in this case. Numerical results are presented to show the effectiveness of the proposed approaches.