TY - JOUR
AU - N. V. Derev’yanko
AU - V. M. Kirilich
PY - 2015/02/25
Y2 - 2022/11/29
TI - Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 2
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1973
AB - 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.
ER -