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The fundamental matrix of solutions of the Cauchy problem for a class of parabolic systems of the Shilov type with variable coefficients

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Abstract

We constructed a fundamental matrix of solutions of the Cauchy problem and studied its basic properties for a new class of linear parabolic systems with smooth bounded variable coefficients that includes a class of the Shilov-type parabolic systems of partial differential equations with nonnegative genus.

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References

  1. S. D. Eidelman, Parabolic Systems, North-Holland, Amsterdam, 1969.

  2. S. D. Eidelman, S. D. Ivasishen, and F. O. Porper, “The Liouville theorems for systems parabolic by Shilov,” Izv. Vyzov. Mat., No. 6, 169–179 (1961).

    Google Scholar 

  3. G. M. Fikhtengolts, A Course of Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow, 1969.

    Google Scholar 

  4. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewoods Cliffs, 1964.

    MATH  Google Scholar 

  5. I. M. Gelfand and G. E. Shilov, Some Questions of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow, 1958.

    Google Scholar 

  6. I. M. Gelfand and G. E. Shilov, Spaces of Basic and Generalized Functions [in Russian], Fizmatgiz, Moscow, 1958.

    Google Scholar 

  7. V. V. Gorodetskii, “Some theorems of the stabilization of solutions of the Cauchy problem for systems parabolic by Shilov in the classes of distributions,” Ukr. Mat. Zh., 40, No. 1, 43–48 (1988).

    Article  MathSciNet  Google Scholar 

  8. U Hou-sin, “On the definition of parabolicity of systems of equations with partial derivatives,” Uspekhi Mat. Nauk, 15, No. 6, 157–161 (1960).

    Google Scholar 

  9. I. G. Petrovskii, “On the Cauchy problem for systems of equations with partial derivatives in a domain of nonanalytic functions,” Bull. MGU. Mat. Mekh., 1, No. 7, 1–72 (1938).

    Google Scholar 

  10. G. E. Shilov, “On the conditions of correctness of the Cauchy problem for systems of partial differential equations with constant coefficients,” Uspekhi Mat. Nauk, 10, No. 4, 89–101 (1955).

    MATH  Google Scholar 

  11. Ya. I. Zhitomirskii, “The Cauchy problem for some types of systems of linear equations with partial derivatives with continuous coefficients parabolic by Shilov,” Izv. AN SSSR. Ser. Mat., 23, 925–932 (1959).

    Google Scholar 

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Authors and Affiliations

  1. Yurii Fed’kovych Chernivtsi National University, 2, Kotsyubyns’kyi Str., Chernivtsi, 58012, Ukraine

    Vladyslav A. Litovchenko & Iryna M. Dovzhitska

Authors
  1. Vladyslav A. Litovchenko
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  2. Iryna M. Dovzhitska
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Corresponding author

Correspondence to Vladyslav A. Litovchenko.

Additional information

Translated from Ukrains’ki˘ı Matematychny˘ı Visnyk, Vol. 7, No. 4, pp. 516–552, October–November, 2010.

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Litovchenko, V.A., Dovzhitska, I.M. The fundamental matrix of solutions of the Cauchy problem for a class of parabolic systems of the Shilov type with variable coefficients. J Math Sci 175, 450–476 (2011). https://doi.org/10.1007/s10958-011-0356-0

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  • DOI: https://doi.org/10.1007/s10958-011-0356-0

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