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Degenerate parabolic systems of vector order Kolmogorov-type equations

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Abstract

We define a new class of degenerate \(\overrightarrow {2b}\)-parabolic systems of Kolmogorov-type equations with coefficients depending only on time. We also construct a fundamental matrix of solutions to a Cauchy problem for systems of this class and study its main properties.

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References

  1. Kolmogoroff A. N., “Zufällige Bewegungen (Zur Theorie der Brownshen Bewegung),” Ann. Math., Bd 35, 116–117 (1934).

    Article  MathSciNet  Google Scholar 

  2. Eidelman S. D., Ivasyshen S. D., and Kochubei A. N., Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type (Oper. Theory, Adv. Appl.), Birkhäuser-Verlag, Basel, Boston, and Berlin (2004).

    Book  Google Scholar 

  3. Malyts’ka H. P., “Systems of equations of Kolmogorov type,” Ukrainian Math. J., 60, No. 12, 1937–1954 (2008).

    Article  MathSciNet  Google Scholar 

  4. Gelfand I. M. and Shilov G. E., Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  5. Gantmakher F. R., The Theory of Matrices [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  6. Gelfand I. M. and Shilov G. E., Certain Problems of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  7. Friedman A., Partial Differential Equations of Parabolic Type [Russian translation], Mir, Moscow (1968).

    Google Scholar 

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Authors and Affiliations

  1. Chernivtsi National University, Chernivtsi, Ukraine

    V. A. Litovchenko & E. B. Nastasiĭ

Authors
  1. V. A. Litovchenko
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  2. E. B. Nastasiĭ
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Corresponding author

Correspondence to V. A. Litovchenko.

Additional information

Original Russian Text Copyright © 2012 Litovchenko V. A. and Nastasiĭ E. B.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 1, pp. 148–164, January–February, 2012.

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Litovchenko, V.A., Nastasiĭ, E.B. Degenerate parabolic systems of vector order Kolmogorov-type equations. Sib Math J 53, 119–133 (2012). https://doi.org/10.1134/S0037446612010107

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  • DOI: https://doi.org/10.1134/S0037446612010107

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