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Sets invariant under an integral constraint on controls

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Abstract

In this paper we study the invariance of given sets with respect to a system with distributed parameters. The considered system is described by a heat conductivity equation whose right-hand side written in the additive form contains a control. For the initial data we obtain sufficient conditions for the strong and weak invariance of the set that represents the graph of a given multivalued mapping.

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Authors and Affiliations

  1. National University of Uzbekistan, Vuzgorodok, Tashkent, 100174, Republic of Uzbekistan

    M. Tukhtasinov

  2. South Kazakhstan State University, ul. Tauke Khana 5, Shymkent, 160019, Republic of Kazakhstan

    U. Ibragimov

Authors
  1. M. Tukhtasinov
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  2. U. Ibragimov
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Corresponding author

Correspondence to M. Tukhtasinov.

Additional information

Original Russian Text © M. Tukhtasinov and U. Ibragimov, 2011, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, No. 8, pp. 69–76.

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Tukhtasinov, M., Ibragimov, U. Sets invariant under an integral constraint on controls. Russ Math. 55, 59–65 (2011). https://doi.org/10.3103/S1066369X11080093

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  • DOI: https://doi.org/10.3103/S1066369X11080093

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