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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2013, Volume 54, Issue 2, Pages 97–105 (Mi pmtf1202)  

This article is cited in 22 scientific papers (total in 22 papers)

Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration

A. L. Kazakov, A. A. Lempert

Institute of System Dynamics and Control Theory, Siberian Branch, Russian Academy of Science, Irkutsk, 664033, Russia
Abstract: The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed.
Keywords: nonlinear filtration, partial differential equations, boundary-value problem, existence and uniqueness theorem, series, convergence.
Received: 08.08.2012
English version:
Journal of Applied Mechanics and Technical Physics, 2013, Volume 54, Issue 2, Pages 251–258
DOI: https://doi.org/10.1134/S0021894413020107
Bibliographic databases:
Document Type: Article
UDC: 533.546:517.957
Language: Russian
Citation: A. L. Kazakov, A. A. Lempert, “Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration”, Prikl. Mekh. Tekh. Fiz., 54:2 (2013), 97–105; J. Appl. Mech. Tech. Phys., 54:2 (2013), 251–258
Citation in format AMSBIB
\Bibitem{KazLem13}
\by A.~L.~Kazakov, A.~A.~Lempert
\paper Existence and uniqueness of the solution of the boundary-value problem for a parabolic equation of unsteady filtration
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2013
\vol 54
\issue 2
\pages 97--105
\mathnet{http://mi.mathnet.ru/pmtf1202}
\elib{https://elibrary.ru/item.asp?id=20653876}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2013
\vol 54
\issue 2
\pages 251--258
\crossref{https://doi.org/10.1134/S0021894413020107}
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  • https://www.mathnet.ru/eng/pmtf/v54/i2/p97
  • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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