On the global boundary stabilization of the Camassa–Holm equation

In the present paper, the boundary stabilization for the Camassa–Holm equation, which describes a generalized formulation for the shallow water wave equation, on an interval is investigated. This is a natural first step towards developing methods for control of flows. We derive nonlinear boundary control laws that achieve global asymptotic stability. We consider both the viscous and the inviscid Camassa–Holm equation, using both higher order boundary control and Dirichlet boundary control.