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Matematicheskie Trudy, 2018, Volume 21, Number 1, Pages 125–154
DOI: https://doi.org/10.17377/mattrudy.2018.21.106 (Mi mt334) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The Cauchy problem for one equation of Sobolev type

A. L. Pavlovab

a Donetsk National University, Donetsk, 283001 Ukraine
b Insititute of Applied Mathematics and Mechanics, Donetsk, 283114 Ukraine
Full-text PDF (285 kB) Citations (6)
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DOI: https://doi.org/10.17377/mattrudy.2018.21.106
Abstract: We give necessary and sufficient conditions for the existence of a solution to the Cauchy problem for the equation Δk∂2tu+(−1)ku=0 in the space of tempered distributions.
Key words: Cauchy problem, equation of Sobolev type, regularization of a distribution.
Received: 12.05.2017
English version:
Siberian Advances in Mathematics, 2019, Volume 29, Issue 1, Pages 57–76
DOI: https://doi.org/10.3103/S105513441901005X
Bibliographic databases:
Document Type: Article
UDC: 517.955
Language: Russian
Citation: A. L. Pavlov, “The Cauchy problem for one equation of Sobolev type”, Mat. Tr., 21:1 (2018), 125–154; Siberian Adv. Math., 29:1 (2019), 57–76
Citation in format AMSBIB
\Bibitem{Pav18}
\by A.~L.~Pavlov
\paper The Cauchy problem for one equation of Sobolev type
\jour Mat. Tr.
\yr 2018
\vol 21
\issue 1
\pages 125--154
\mathnet{http://mi.mathnet.ru/mt334}
\crossref{https://doi.org/10.17377/mattrudy.2018.21.106}
\elib{https://elibrary.ru/item.asp?id=34878268}
\transl
\jour Siberian Adv. Math.
\yr 2019
\vol 29
\issue 1
\pages 57--76
\crossref{https://doi.org/10.3103/S105513441901005X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85064761607}
Linking options:
  • https://www.mathnet.ru/eng/mt334
  • https://www.mathnet.ru/eng/mt/v21/i1/p125
    • This publication is cited in the following 6 articles:
    1. Andreas Chatziafratis, Tohru Ozawa, “New instability, blow-up and break-down effects for Sobolev-type evolution PDE: asymptotic analysis for a celebrated pseudo-parabolic model on the quarter-plane”, Partial Differ. Equ. Appl., 5:5 (2024)  crossref
    2. A. L. Pavlov, “Regularization of distributions”, Sb. Math., 214:4 (2023), 516–549  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. A. L. Pavlov, “Regulyarizatsiya obobschennoi funktsii, golomorfno zavisyaschei ot parametra”, Sib. matem. zhurn., 64:6 (2023), 1279–1303  mathnet  crossref
    4. A. L. Pavlov, “Regularization of a Distribution Holomorphic in a Parameter”, Sib Math J, 64:6 (2023), 1399  crossref
    5. A. L. Pavlov, “The solvability of the Cauchy problem for a class of Sobolev-type equations in tempered distributions”, Siberian Math. J., 63:5 (2022), 940–955  mathnet  crossref  crossref
    6. A. L. Pavlov, “Existence of solutions to the Cauchy problem for some class of Sobolev-type equations in the space of tempered distributions”, Siberian Math. J., 60:4 (2019), 644–660  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    References:60
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