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Fundam. Prikl. Mat., 2006, Volume 12, Issue 4, Pages 169–186 (Mi fpm965)  

This article is cited in 4 scientific papers (total in 4 papers)

On stabilization of solutions of singular elliptic equations

A. B. Muravnik

Information Center of 4th Poliklinik of Voronezh

Abstract: Linear and quasi-linear elliptic equations containing the Bessel operator with respect to a selected variable (so-called special variable) are studied. The well-posedness of the nonclassical Dirichlet problem (with the additional condition of evenness with respect to the special variable) in the half-space is proved, an integral representation of the solution is constructed, and a necessary and sufficient condition of the stabilization is established. The stabilization is understood as follows: the solution has a finite limit as the independent variable tends to infinity along the direction orthogonal to the boundary hyperplane.

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English version:
Journal of Mathematical Sciences (New York), 2008, 150:5, 2408–2421

Bibliographic databases:

UDC: 517.956

Citation: A. B. Muravnik, “On stabilization of solutions of singular elliptic equations”, Fundam. Prikl. Mat., 12:4 (2006), 169–186; J. Math. Sci., 150:5 (2008), 2408–2421

Citation in format AMSBIB
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\by A.~B.~Muravnik
\paper On stabilization of solutions of singular elliptic equations
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 4
\pages 169--186
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\zmath{https://zbmath.org/?q=an:1151.35370}
\elib{http://elibrary.ru/item.asp?id=11143782}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 150
\issue 5
\pages 2408--2421
\crossref{https://doi.org/10.1007/s10958-008-0139-4}
\elib{http://elibrary.ru/item.asp?id=14551201}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42149192059}


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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. A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem”, Journal of Mathematical Sciences, 216:3 (2016), 345–496  mathnet  crossref
    2. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
    3. A. B. Muravnik, “On qualitative properties of solutions to quasilinear parabolic equations admitting degenerations at infinity”, Ufa Math. J., 10:4 (2018), 77–84  mathnet  crossref  isi
    4. A. B. Muravnik, “O kachestvennykh svoistvakh znakopostoyannykh reshenii nekotorykh kvazilineinykh parabolicheskikh zadach”, Materialy mezhdunarodnoi konferentsii«InternationalConference onMathematicalModellinginAppliedSciences, ICMMAS-17», Sankt-Peterburgskii politekhnicheskii universitet,2428 iyulya2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 160, VINITI RAN, M., 2019, 85–94  mathnet
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