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Mat. Sb. (N.S.), 1981, Volume 115(157), Number 4(8), Pages 532–543 (Mi msb2414)  

This article is cited in 5 scientific papers (total in 5 papers)

On a problem with free boundary for parabolic equations

A. M. Meirmanov


Abstract: This paper considers the problem of determining a solution of the parabolic equation
$$ L\theta\equiv D_t\theta-\sum^2_{i,j=1}D_i(a_{ij}(x,t,\theta)\cdot D_j\theta)+a(x,t,\theta,D\theta)=0 $$
and the boundary of the two-dimensional region in which a solution of the equation is sought in the case where on the free boundary the value of the desired function and the additional condition
$$ \sum^2_{i,j=1}a_{ij}D_i\theta\cdot D_j\theta=g(x,t) $$
are satisfied.
For this problem a theorem asserting the existence of a smooth solution on a small time interval is proved. If $L\theta=0$ is the heat equation, then the solution exists on any time interval, and it is unique.
Bibliography: 7 titles.

Full text: PDF file (1134 kB)
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English version:
Mathematics of the USSR-Sbornik, 1982, 43:4, 473–484

Bibliographic databases:

UDC: 517.946+536.42
MSC: Primary 35K20; Secondary 76S05
Received: 13.10.1980

Citation: A. M. Meirmanov, “On a problem with free boundary for parabolic equations”, Mat. Sb. (N.S.), 115(157):4(8) (1981), 532–543; Math. USSR-Sb., 43:4 (1982), 473–484

Citation in format AMSBIB
\Bibitem{Mei81}
\by A.~M.~Meirmanov
\paper On~a~problem with free boundary for parabolic equations
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 115(157)
\issue 4(8)
\pages 532--543
\mathnet{http://mi.mathnet.ru/msb2414}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=629625}
\zmath{https://zbmath.org/?q=an:0503.35083|0492.35076}
\transl
\jour Math. USSR-Sb.
\yr 1982
\vol 43
\issue 4
\pages 473--484
\crossref{https://doi.org/10.1070/SM1982v043n04ABEH002575}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Crowley A., Ockendon J., “Modeling Mushy Regions”, Appl. Sci. Res., 44:1-2 (1987), 1–7  crossref  isi
    2. Howison S., Lacey A., Ockendon J., “Hele-Shaw Free-Boundary Problems with Suction”, Q. J. Mech. Appl. Math., 41:2 (1988), 183–193  crossref  mathscinet  isi
    3. Victor A. Galaktionoy, Josephus Hulshof, Juan L. Vazquez, “Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem”, Journal de Mathématiques Pures et Appliquées, 76:7 (1997), 563  crossref
    4. Petrosyan A., “On Existence and Uniqueness in a Free Boundary Problem From Combustion”, Commun. Partial Differ. Equ., 27:3-4 (2002), 763–789  crossref  mathscinet  zmath  isi
    5. Kim I., “A Free Boundary Problem Arising in Flame Propagation”, J. Differ. Equ., 191:2 (2003), 470–489  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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