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

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

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
\Bibitem{Lit05} \by V.~A.~Litovchenko \paper Cauchy problem for $\{\vec p;\vec h\}$-parabolic equations with time-dependent coefficients \jour Mat. Zametki \yr 2005 \vol 77 \issue 3 \pages 395--411 \mathnet{http://mi.mathnet.ru/mz2501} \crossref{https://doi.org/10.4213/mzm2501} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2157899} \zmath{https://zbmath.org/?q=an:1077.35054} \elib{http://elibrary.ru/item.asp?id=9150080} \transl \jour Math. Notes \yr 2005 \vol 77 \issue 3 \pages 364--379 \crossref{https://doi.org/10.1007/s11006-005-0036-9} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000228965300007} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-20244378380} 

• http://mi.mathnet.ru/eng/mz2501
• 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
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
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
4. Litovchenko V.A., “Parabolic By Shilov Systems With Variable Coefficients”, Carpathian Math. Publ., 9:2 (2017), 145–153
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
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
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
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