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Siberian Mathematical Journal

, Volume 45, Issue 4, pp 669–679 | Cite as

The Cauchy Problem for Shilov Parabolic Equations

  • V. A. Litovchenko
Article

Abstract

We establish well-posed solvability of the Cauchy problem for the Shilov parabolic equations with time-dependent coefficients whose initial data are tempered distributions. For a certain class of equations we state necessary and sufficient conditions for unique solvability of the Cauchy problem whose properties with respect to the spatial variable are typical for a fundamental solution. The results are characterized only by the order and the parabolicity exponent.

Cauchy problem Shilov parabolicity S-type space multiplier 

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References

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    Gelfand I. M. and Shilov G. E., Spaces of Test and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
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    Gelfand I. M. and Shilov G. E., Certain Problems of the Theory of Differential Equations [in Russian], Fizmatgiz, Moscow (1958).Google Scholar
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    Gorodetski?i V. V. and Zhitaryuk I. V., “On the rate of localization of solutions of the Cauchy problem for parabolic equations with degeneration,” Differentsial0nye Uravneniya, 27, No. 4, 697–699 (1991).Google Scholar
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    Borok V. M., “ solution of the Cauchy problem for some types of systems of linear partial differential equations,” Dokl. Akad. Nauk SSSR, 97, No. 6, 949–952 (1954).Google Scholar

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • V. A. Litovchenko
    • 1
  1. 1.Chernovtsy National University, theUkraine

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