2017
Том 69
№ 9

All Issues

Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning

Derev’yanko N. V., Kirilich V. M.


Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 2, pp 211-229.

Citation Example: Derev’yanko N. V., Kirilich V. M. Problem of Optimal Control for a Semilinear Hyperbolic System of Equations of the First Order with Infinite Horizon Planning // Ukr. Mat. Zh. - 2015. - 67, № 2. - pp. 185–201.