On the optimal control problem for the Novikov equation with strong viscosity

Abstract

Please cite this article in press as: J. Zhou et al., On the optimal control problem for the Novikov equation with strong viscosity, Highlights• The existence of a unique weak solution to the viscous Novikov equation is obtained.• The existence of an optimal solution to the optimal control problem is shown. • The first-order necessary optimality condition is deduced.• Two second-order sufficient optimality conditions are established. AbstractIn 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.

Stability and bifurcation analysis on a delayed epidemic model with information-dependent vaccination

“…Investigating the diffusion law of epidemics is to help the government take effective measures to decline the number of the infected people and enhance the number of the cured people by the minimum cost [39][40][41][42]. For this purpose, in the following we will consider the optimal control problem of system (1.3).…”