Journal of Dynamical and Control Systems

, Volume 19, Issue 3, pp 381–404 | Cite as

On Vector-Valued Approximation of State Constrained Optimal Control Problems for Nonlinear Hyperbolic Conservation Laws

  • P. I. Kogut
  • R. Manzo


We study one class of nonlinear fluid dynamic models with controls in the initial condition and the source term. The model is described by a nonlinear inhomogeneous hyperbolic conservation law with state and control constraints. We consider the case when the greatest lower bound of the cost functional can be unattainable on the set Ξ of admissible pairs or the set Ξ is possibly empty. Using the methods of vector-valued optimization theory, we show that this optimal control problem admits the existence of the so-called weakened approximate solution which can be interpreted as generalized solution to some vector optimization problem of special form.

2000 Mathematics Subject Classification

46B40 49J45 90C29 49N90 76N15 

Key words and phrases

Nonlinear conservation laws control and state constraints vector optimization problem weakened approximate solutions entropy solutions 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Differential EquationsDnipropetrovsk National UniversityDnipropetrovskUkraine
  2. 2.Dipartimento di Ingegneria Elettronica e Ingegneria InformaticaUniversità degli Studi di SalernoFisciano (SA)Italy

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