Maximum principle for optimal boundary control of the Kuramoto–Sivashinsky equation

In this paper, the optimal boundary control for the Kuramoto–Sivashinsky equation is considered. The Dubovitskii and Milyutin functional analytical approach is adopted in investigation of Pontryaginʹs maximum principles of the system in both fixed and free final horizon cases. The necessary conditions are, respectively, presented for the optimal boundary control problems in these two cases.