Ukrainian Mathematical Journal

, Volume 67, Issue 2, pp 211–229 | Cite as

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

  • T. O. Derev’yanko
  • V. M. Kyrylych

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.


Optimal Control Problem Hyperbolic System Boundary Control Exponential Dichotomy Adjoint Problem 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • T. O. Derev’yanko
    • 1
  • V. M. Kyrylych
    • 1
  1. 1.Franko Lviv National UniversityLvivUkraine

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