@article{Derev’yanko_Kirilich_2015, title={Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning}, volume={67}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1973}, abstractNote={We establish necessary conditions for the optimality of smooth boundary and initial controls in a semilinear hyperbolic system of the first order. The problem adjoint to the original problem is a semilinear hyperbolic system without initial conditions. The suggested approach is based on the use of special variations of continuously differentiable controls. The existence of global generalized solutions for a semilinear first-order hyperbolic system in a domain unbounded in time is proved. The proof is based on the use of the Banach fixed-point theorem and a space metric with weight functions.}, number={2}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Derev’yanko, N. V. and Kirilich, V. M.}, year={2015}, month={Feb.}, pages={185–201} }