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On a differential game in a system with distributed parameters

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Abstract

We consider a game problem of approach for a system whose dynamics is described by a partial differential equation not of Kovalevskaya type, i.e., unsolved with respect to the time derivative. The equation with boundary conditions is written in a Hilbert function space in an abstract form as a differential operator equation. Using the method of resolving functionals, we obtain sufficient conditions for the approach of the system’s dynamical vector to a cylindrical terminal set. The results are exemplified by means of a model problem concerning a filtering process for a fluid in fractured porous rocks.

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Authors and Affiliations

  1. Kharkov National University, pl. Svobody 4, Kharkov, 61022, Ukraine

    L. A. Vlasenko

  2. Institute of Cybernetics, National Academy of Sciences of Ukraine, pr. Akad. Glushkova 40, Kiev, 03680, Ukraine

    A. A. Chikrii

Authors
  1. L. A. Vlasenko
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  2. A. A. Chikrii
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Correspondence to L. A. Vlasenko.

Additional information

Original Russian Text © L.A. Vlasenko, A.A. Chikrii, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 4.

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Vlasenko, L.A., Chikrii, A.A. On a differential game in a system with distributed parameters. Proc. Steklov Inst. Math. 292 (Suppl 1), 276–285 (2016). https://doi.org/10.1134/S0081543816020243

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