International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 297-311

On the existence of a solution for some distributed optimal control hyperbolic system

Dariusz Idczak and Stanisław Walczak

Institute of Mathematics, Łódź University, ul. Stefana Banacha 22, Łódź 90-238, Poland

Received 12 December 1994; Revised 30 March 1995

Copyright © 2000 Dariusz Idczak and Stanisław Walczak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. We prove a theorem on the existence of an optimal process in the classes of absolutely continuous trajectories of two variables and measurable controls with values in a fixed compact and convex set.