  In this paper, we investigate the optimal control problem for the k-FORQ/MCH
equation with strong viscosity.We prove the existence and uniqueness of this
equation under the initial and boundary conditions by Galerkin method. From
these results and the Lion's theory we deduce the existence of an optimal
solution to the control problem governed by the viscous k-FORQ/MCH equation.
Using augmented Lagrangian method, we deduce the first-order necessary
optimality condition and two second-order sufficient optimality conditions.
