Optimal control of the viscous weakly dispersive Degasperis–Procesi equation

In this paper, we study the optimal control problem for the viscous weakly dispersive Degasperis–Procesi equation. We deduce the existence and uniqueness of a weak solution to this equation in a short interval by using the Galerkin method. Then, according to optimal control theories and distributed parameter system control theories, the optimal control of the viscous weakly dispersive Degasperis–Procesi equation under boundary conditions is given and the existence of an optimal solution to the viscous weakly dispersive Degasperis–Procesi equation is proved.