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A Class of Semilinear Degenerate Equations with Fractional Lower Order Derivatives

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Stability, Control and Differential Games

Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

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Abstract

Unique solution existence is proved for the generalized Showalter–Sidorov problem to semilinear evolution equations with a degenerate linear operator at the highest fractional Gerasimov–Caputo derivative and with some constraints on the nonlinear operator. The nonlinear operator in the equation depends on lower order fractional derivatives. Abstract result is used for the study of an initial boundary value problem for the system of the dynamics of Kelvin–Voigt viscoelastic fluid, in which rheological relation is defined by a fractional order equation.

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Acknowledgements

The reported study was funded by Act 211 of Government of the Russian Federation, contract 02.A03.21.0011, and by Ministry of Science and Higher Education of the Russian Federation, task number 1.6462.2017/BCh.

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Authors and Affiliations

  1. South Ural State University, Chelyabinsk, Russia

    Marina V. Plekhanova

  2. Chelyabinsk State University, Chelyabinsk, Russia

    Marina V. Plekhanova & Guzel D. Baybulatova

Authors
  1. Marina V. Plekhanova
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  2. Guzel D. Baybulatova
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Corresponding author

Correspondence to Marina V. Plekhanova .

Editor information

Editors and Affiliations

  1. UrB RAS, IIASA, Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Alexander Tarasyev

  2. UrB RAS, Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Vyacheslav Maksimov

  3. UrB RAS, Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Tatiana Filippova

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Plekhanova, M.V., Baybulatova, G.D. (2020). A Class of Semilinear Degenerate Equations with Fractional Lower Order Derivatives. In: Tarasyev, A., Maksimov, V., Filippova, T. (eds) Stability, Control and Differential Games. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-42831-0_18

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