Boundary control of multi-dimensional discrete-velocity kinetic models

This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive feasible control laws so that the corresponding solutions decay exponentially in time. The result is illustrated with an application to the two-dimensional coplanar model in a square container. The effectiveness of the derived control laws is confirmed by numerical simulations.