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Mat. Zametki, 2005, Volume 77, Issue 3, Pages 395–411 (Mi mz2501)  

This article is cited in 7 scientific papers (total in 7 papers)

Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients

V. A. Litovchenko

Chernivtsi National University named after Yuriy Fedkovych

Abstract: We establish the existence of a unique solution continuously depending on the initial data to the Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients for which the initial data are generalized functions (distributions) of slow growth. For a particular class of equations, we state necessary and sufficient conditions for the existence of a unique solution of the Cauchy problem with properties of its spatial variable which are characteristic of its fundamental solution.

DOI: https://doi.org/10.4213/mzm2501

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English version:
Mathematical Notes, 2005, 77:3, 364–379

Bibliographic databases:

UDC: 517.55
Received: 08.10.2002

Citation: V. A. Litovchenko, “Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients”, Mat. Zametki, 77:3 (2005), 395–411; Math. Notes, 77:3 (2005), 364–379

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm2501
  • http://mi.mathnet.ru/eng/mz/v77/i3/p395

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Litovchenko, “Cauchy Problem for Parabolic Systems with Convolution Operators in Periodic Spaces”, Math. Notes, 82:6 (2007), 766–786  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Ivasyshen S.D., Litovchenko V.A., “Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type with positive genus”, Ukrainian Math. J., 61:8 (2009), 1264–1288  crossref  mathscinet  zmath  isi  elib  scopus
    3. Ivasyshen S.D., Litovchenko V.A., “Cauchy problem for a class of degenerate Kolmogorov-type parabolic equations with nonpositive genus”, Ukrainian Math. J., 62:10 (2011), 1543–1566  crossref  mathscinet  zmath  isi  elib  scopus
    4. Litovchenko V.A., “Parabolic By Shilov Systems With Variable Coefficients”, Carpathian Math. Publ., 9:2 (2017), 145–153  crossref  mathscinet  zmath  isi
    5. Litovchenko V.A., Unguryan G.M., “Parabolic Systems of Shilov-Type With Coefficients of Bounded Smoothness and Nonnegative Genus”, Carpathian Math. Publ., 9:1 (2017), 72–85  crossref  mathscinet  zmath  isi
    6. Litovchenko V.A., Unguryan G.M., “Conjugate Cauchy Problem For Parabolic Shilov Type Systems With Nonnegative Genus”, Differ. Equ., 54:3 (2018), 335–351  crossref  mathscinet  zmath  isi  scopus  scopus
    7. Litovchenko V.A., “One Method For the Investigation of Fundamental Solution of the Cauchy Problem For Parabolic Systems”, Ukr. Math. J., 70:6 (2018), 922–934  crossref  mathscinet  isi  scopus
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