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Problems of Hard Control for a Class of Degenerate Fractional Order Evolution Equations

  • Marina V. PlekhanovaEmail author
  • Guzel D. Baybulatova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11548)

Abstract

We find conditions of unique strong solution existence for the generalized Showalter—Sidorov problem to semilinear evolution equations with a degenerate operator at the highest fractional Gerasimov—Caputo derivative and with some constraint on the image of the nonlinear operator. Then we consider a class of optimal control problems for systems, whose dynamics is described by such equations endowed with the respective initial value conditions. Target functional is assumed not to take into account control costs. In such situation we used the additional condition of the admissible controls set boundedness. The obtained result of the initial problem unique solvability and properties of some functions spaces are applied to the proof of optimal control existence for such class of problems. Abstract results are applied to study of a control problem for a system, which is described by an initial-boundary value problem to a nonlinear partial differential equation, not solvable with respect to the highest time fractional derivative.

Keywords

Optimal control problem Distributed control system Semilinear degenerate evolution equation Fractional derivative Strong solution Initial-boundary value problem 

Notes

Acknowledgements

The work is supported by Act 211 of Government of the Russian Federation, contract 02.A03.21.0011, and by Ministry of Education and Science of the Russian Federation, task No 1.6462.2017/BCh.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.South Ural State UniversityChelyabinskRussia
  2. 2.Chelyabinsk State UniversityChelyabinskRussia

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