An optimal distributed control problem of the viscous Degasperis-Procesi equation

This paper is concerned with an optimal distributed control problem of the viscous Degasperis–Procesi equation. The Dubovitskii and Milyutin functional analytical approach is adopted in the investigation of the Pontryagin maximum principle of the system. The necessary condition for optimality is established for the problem in the fixed final horizon case and, subsequently, a remark on the applicability of the obtained results is made for illustration.

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