On boundary optimal control problem for an arterial system: Existence of feasible solutions

On boundary optimal control problem for an arterial system: First-order optimality conditions

“…Optimal control problem (1)- (5) comes from the fluid dynamic models of blood flows in arterial systems. It is well known that the cardiovascular system consists of a pump that propels a viscous liquid (the blood) through a network of flexible tubes.…”

“…In the first part of our investigation (see [5]) we make use of the standard viscous hyperbolic system (see [2,21]) which models cross-section area S(x, t) and average velocity u(x, t) in the spatial domain:…”

“…), which play a crucial role in the proof of solvability of OCP (1)- (5). In this paper we deal with the existence of optimal solutions and derive the corresponding optimality conditions for the problem (1)- (5).…”

“…), which play a crucial role in the proof of solvability of OCP (1)- (5). In this paper we deal with the existence of optimal solutions and derive the corresponding optimality conditions for the problem (1)- (5). It should be mentioned, that application of Lagrange principle requires even higher smoothness of solutions to the initial Boussinesq system (2)- (4).…”

“…It should be mentioned, that application of Lagrange principle requires even higher smoothness of solutions to the initial Boussinesq system (2)- (4). In order to avoid such limitations, we deal with a simplified version of the initial optimal control problem (2)-(4) (see (39), argumentation above and [3,5] for physical description of the considered model). Also, in the second part of the paper, in order to provide the thorough substantiation of the first-order optimality conditions to the considered OCP, we make the special assumption for δ to be an element of the class H 1 (Ω).…”