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Journal of Optimization Theory and Applications

, Volume 180, Issue 1, pp 303–320 | Cite as

Optimal Control Problem for Bianchi Equation in Variable Exponent Sobolev Spaces

  • Rovshan A. BandaliyevEmail author
  • Vagif S. Guliyev
  • Ilgar G. Mamedov
  • Yasin I. Rustamov
Article
  • 69 Downloads

Abstract

In this paper, a necessary and sufficient condition, such as the Pontryagin’s maximum principle for an optimal control problem with distributed parameters, is given by the third-order Bianchi equation with coefficients from variable exponent Lebesgue spaces. The statement of an optimal control problem is studied by using a new version of the increment method that essentially uses the concept of the adjoint equation of the integral form.

Keywords

3D optimal control Pontryagin’s maximum principle Bianchi equation Goursat problem Variable exponent Sobolev spaces 

Mathematics Subject Classification

37D30 49B20 49K20 

Notes

Acknowledgements

The authors thank the anonymous reviewers for their careful reading of our manuscript and their valuable comments and suggestions, which helped to improve the manuscript. The research of R. Bandaliyev and V.S. Guliyev was partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement number: 02.a03.21.0008) and by the Grant of Presidium of Azerbaijan National Academy of Science 2015.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Rovshan A. Bandaliyev
    • 1
    • 2
    Email author
  • Vagif S. Guliyev
    • 1
    • 2
    • 3
  • Ilgar G. Mamedov
    • 4
  • Yasin I. Rustamov
    • 4
  1. 1.Institute of Mathematics and Mechanics of NAS of AzerbaijanBakuAzerbaijan
  2. 2.S.M. Nikolskii Institute of Mathematics at RUDN UniversityMoscowRussia
  3. 3.Department of MathematicsAhi Evran UniversityKirsehirTurkey
  4. 4.Institute of Control Systems of NAS of AzerbaijanBakuAzerbaijan

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