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Relay control of an evolution process in a Banach space in a neighborhood of an unstable stationary regime

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Abstract

We study a controlled evolution process whose states are characterized by points of a real Banach space and which is described by a family of semigroups in a neighborhood of an unstable stationary regime. The goal is to find control to keep the state of the process however long in the neighborhood. We find conditions under which this control is possible, and prove an existence theorem. Also, we apply the theorem to the processes described by systems of parabolic differential equations.

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References

  1. Musienko E. I., “Controlling a solution to one parabolic problem in a neighborhood of an unstable stationary solution,“ Dinamika Sploshn. Sredy, No. 51, 68–83 (1981).

    MathSciNet  Google Scholar 

  2. Musienko E. I., “Controlling a solution to some parabolic problems in a neighborhood of an unstable stationary solution,“ Differentsialnye Uravneniya, 20, No. 12, 2120–2130 (1984).

    MathSciNet  Google Scholar 

  3. Ivirsin M. B., “Parametric control of solutions to an evolution problem in a neighborhood of an unstable stationary regime,“ Siberian Math. J., 48, No. 4, 606–615 (2007).

    Article  MathSciNet  Google Scholar 

  4. Belonosov V. S. and Zelenyak T. I., Nonlocal Problems in the Theory of Quasilinear Parabolic Equations [in Russian], Novosibirsk Univ., Novosibirsk (1975).

    Google Scholar 

  5. Belonosov V. S., “Estimates of solutions of parabolic systems in weighted Hölder classes and some of their applications,“ Math. USSR-Sb., 38, No. 2, 151–173 (1981).

    Article  MATH  Google Scholar 

  6. Ladyzhenskaya O. A., Solonnikov V. A., and Ural’tseva N. N., Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence (1968).

    Google Scholar 

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Authors and Affiliations

  1. Novosibirsk State University, Novosibirsk, Russia

    M. B. Ivirsin

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  1. M. B. Ivirsin
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Correspondence to M. B. Ivirsin.

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Original Russian Text Copyright © 2010 Ivirsin M. B.

The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00221), the Russian Federal Agency for Education (Grant 2.1.1.4918), and the Presidium of the Russian Academy of Sciences (Fundamental Research Program No. 2).

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 1, pp. 32–47, January–February, 2010.

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Ivirsin, M.B. Relay control of an evolution process in a Banach space in a neighborhood of an unstable stationary regime. Sib Math J 51, 25–37 (2010). https://doi.org/10.1007/s11202-010-0004-9

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  • DOI: https://doi.org/10.1007/s11202-010-0004-9

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