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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
Article
  • 27 Downloads

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.

Keywords

Optimal Control Problem Hyperbolic System Boundary Control Exponential Dichotomy Adjoint Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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