Duality in the optimal control of hyperbolic equations with positive controls (Q1567230)

The paper considers a linear-quadratic optimal control problem for a hyperbolic equation. The authors write a formal optimality system and by simple algebraic calculations (without any proofs that the carried out calculations are permitted) show that the solution of the optimality system defines a saddle point for the original-dual problem. The paper contains inadequate formulae, for instance, the hyperbolic equation is written as \(y_{tt}+\Delta y= u\), \((t,x)\in (0,T)\times \Omega\), the set of initial values is taken from \(H^{-1}(\Omega)\).