International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2000 / Article

Open Access

Volume 23 |Article ID 169637 | 15 pages | https://doi.org/10.1155/S0161171200000880

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

Received12 Dec 1994
Revised30 Mar 1995

Abstract

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.

Copyright © 2000 Hindawi Publishing Corporation. 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.

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