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The Cauchy Problem for a Stochastic Parabolic Equation with an Argument Deviation

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Cybernetics and Systems Analysis Aims and scope

Abstract

The Cauchy problem for a stochastic nonlinear equation of parabolic type with delay is considered. Using Green’s function, a formula is derived for finding the solution of the problem by the method of steps. The existence of a solution is established with probability one and the solution is estimated according to a specially introduced norm.

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References

  1. E. Elsholtz and S. B. Norkin, Introduction to the Theory of Differential Equations with a Deviating Argument [in Russian], Nauka, Moscow (1971).

  2. Ya. M. Drin’ and M. M. Drin’, “Analysis of the Cauchy problem for quasi-linear B-parabolic equations with deviation of the argument,” Nauk. Visnyk Cherniv. Nats. Univ. im. Yuriya Fed’kovycha, Ser. Matem., Vol. 2, No. 1, 32–34 (2012).

    MATH  Google Scholar 

  3. M. I. Matiychuk, Parabolic and Elliptic Problems in Dini Spaces [in Ukrainian], Cherniv. Nats. Univ., Chernivtsi (2010).

  4. A. M. Samoilenko and M. A. Perestyuk, Differential Equations with Impulse Action [in Russian], Vyshcha Shkola, Kyiv (1987).

  5. S. D. Eidelman, Parabolic Systems [in Russian], Nauka, Moscow (1964).

  6. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations [in Russian], Naukova Dumka, Kyiv (1968).

  7. H. M. Perun, “Problem with pulse action for a linear stochastic parabolic equation of higher order,” Ukr. Math. J., Vol. 60, No. 10, 1660–1665 (2008).

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine

    G. Perun & V. Yasynskyy

Authors
  1. G. Perun
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  2. V. Yasynskyy
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Correspondence to G. Perun.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2022, pp. 114–119.

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Perun, G., Yasynskyy, V. The Cauchy Problem for a Stochastic Parabolic Equation with an Argument Deviation. Cybern Syst Anal 58, 952–956 (2022). https://doi.org/10.1007/s10559-023-00529-7

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  • DOI: https://doi.org/10.1007/s10559-023-00529-7

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