Boundary control on the viscous Fornberg–Whitham equation

This paper investigates the problem of boundary control of the viscous Fornberg–Whitham equation. The existence and uniqueness of weak solution to the viscous Fornberg–Whitham equation are proved in a short interval. Moreover, we prove the Fornberg–Whitham equation global exponential stability in L2,H1,H2,H3L2,H1,H2,H3 under the given boundary condition.