Abstract
In this paper, we consider an optimal control problem for the Novikov equation with strong viscosity. Using the Faedo–Galerkin method we derive the existence of a unique weak solution to this equation. Applying Lions' theory, we obtain the existence of an optimal solution to the control problem for this equation. We also deduce the first-order necessary optimality condition. Moreover we establish two second-order sufficient optimality conditions, which require coercivity of the augmented Lagrangian functional on the whole space or on a suitable subspace.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
