Optimal distributed control of the Fornberg–Whitham equation

Abstract In this paper, the optimal distributed control of the Fornberg–Whitham equation is considered. We discuss the existence and uniqueness of a weak solution to the Fornberg–Whitham equation with forcing item in a special Hilbert space S ( 0 , T ) . We also investigate the existence of an optimal control solution to the Fornberg–Whitham equation with the cost functional. Adopting the Dubovitskii–Milyutin functional analytical method, we present necessary optimality condition of optimal control (local maximum principle) for the investigated system in the fixed final horizon case.