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The Cauchy Problem for Shilov Parabolic Equations

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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.

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References

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

    Google Scholar 

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

    Google Scholar 

  3. 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).

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  4. 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 

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Litovchenko, V.A. The Cauchy Problem for Shilov Parabolic Equations. Siberian Mathematical Journal 45, 669–679 (2004). https://doi.org/10.1023/B:SIMJ.0000035831.63036.bb

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000035831.63036.bb

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