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Mat. Sb. (N.S.), 1986, Volume 131(173), Number 4(12), Pages 477–500 (Mi msb1974)  

This article is cited in 20 scientific papers (total in 20 papers)

The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients

Yu. A. Alkhutov, I. T. Mamedov


Abstract: This paper is concerned with the questions of solvability and smoothness of weak solutions of the first boundary value problem for a parabolic equation of the form
$$ \mathscr Lu=\sum^n_{i,k=1}a_{ik}(t,x)u_{x_ix_k}-u_t=f(t,x). $$

Bibliography: 18 titles.

Full text: PDF file (1044 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1988, 59:2, 471–495

Bibliographic databases:

UDC: 517.956.4
MSC: Primary 35K20; Secondary 35B65, 35R05
Received: 04.07.1985 and 27.05.1986

Citation: Yu. A. Alkhutov, I. T. Mamedov, “The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients”, Mat. Sb. (N.S.), 131(173):4(12) (1986), 477–500; Math. USSR-Sb., 59:2 (1988), 471–495

Citation in format AMSBIB
\Bibitem{AlkMam86}
\by Yu.~A.~Alkhutov, I.~T.~Mamedov
\paper The first boundary value problem for nondivergence second order parabolic equations with discontinuous coefficients
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 131(173)
\issue 4(12)
\pages 477--500
\mathnet{http://mi.mathnet.ru/msb1974}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=881909}
\zmath{https://zbmath.org/?q=an:0663.35033}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 59
\issue 2
\pages 471--495
\crossref{https://doi.org/10.1070/SM1988v059n02ABEH003147}


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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. Kamynin V., “Asymptotic-Behavior of Solutions of the Cauchy-Problem for Non-Divergence Parabolic Equations”, 316, no. 4, 1991, 807–811  mathscinet  zmath  isi
    2. Kamynin V., “Passage to the Limit in the Inverse Problem for Nondivergent Parabolic Equations with a Final Overdetermination Condition”, Differ. Equ., 28:2 (1992), 213–218  mathnet  mathscinet  zmath  isi
    3. Gasanova I., “On the Holder Property of Derivatives of Solutions to 2nd-Order Parabolic Equations in Nontube Domains”, Differ. Equ., 30:1 (1994), 100–109  mathnet  mathscinet  zmath  isi
    4. Guochun Wen, Benteng Zou, “Estimates of solutions of initial-irregular oblique derivative problems for linear parabolic equations of second order with measurable coefficients”, Sci China Ser A, 41:11 (1998), 1163  crossref  mathscinet  zmath
    5. Guochun Wen, Maoying Tain, “Initial-oblique derivative problems for nonlinear parabolic equations with measurable coefficients”, Communications in Nonlinear Science and Numerical Simulation, 3:2 (1998), 109  crossref  mathscinet  zmath
    6. Guochun Wen, “Initial-irregular oblique derivative problems for nonlinear parabolic systems of second order equations with measurable coefficients”, Sci China Ser A, 42:7 (1999), 681  crossref  mathscinet  zmath
    7. Guochun Wen, Zuoliang Xu, “Oblique derivative problems for nonlinear elliptic systems with measurable coefficients”, Communications in Nonlinear Science and Numerical Simulation, 6:2 (2001), 93  crossref  mathscinet  zmath
    8. V. L. Kamynin, “On the Unique Solvability of an Inverse Problem for Parabolic Equations under a Final Overdetermination Condition”, Math. Notes, 73:2 (2003), 202–211  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. L. Kamynin, “On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition”, Math. Notes, 77:4 (2005), 482–493  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Guochun Wen, Dechang Chen, “Oblique derivative boundary value problems for nonlinear elliptic equations of second order with measurable coefficients in high dimensional domains”, Communications in Nonlinear Science and Numerical Simulation, 10:5 (2005), 559  crossref  mathscinet  zmath
    11. Guo Chun Wen, DeChang Chen, “Mixed boundary value problems for nonlinear elliptic equations of second order with measurable coefficients in high dimensional domains”, Complex Variables, 51:3 (2006), 267  crossref  mathscinet  zmath
    12. Guochun Wen, Dechang Chen, “Some boundary value problems for nonlinear elliptic equations of second order in high-dimensional domains”, Applicable Analysis, 85:9 (2006), 1011  crossref  mathscinet  zmath
    13. Gadjiev T.S., Gasimova E.R., “On the Smoothness of a Solution of the First Boundary-Value Problem for Second-Order Degenerate Elliptic-Parabolic Equations”, Ukr. Math. J., 60:6 (2008), 831–847  crossref  mathscinet  zmath  isi
    14. BOUBAKER-KHALED SADALLAH, “REGULARITY OF A PARABOLIC EQUATION SOLUTION IN A NONSMOOTH AND UNBOUNDED DOMAIN”, JAZ, 84:02 (2008)  crossref  mathscinet  zmath
    15. Erisova I.A., “Convergence of Solutions of Backward Stochastic Equations”, Ukr. Math. J., 61:7 (2009), 1093–1112  crossref  mathscinet  zmath  isi
    16. I. T. Mamedov, “First boundary-value problem for second-order elliptic-parabolic equations with discontinuous coefficients”, Journal of Mathematical Sciences, 190:1 (2013), 104–134  mathnet  crossref  mathscinet
    17. Kamynin V.L., “Ob odnoznachnoi razreshimosti obratnoi zadachi opredeleniya starshego koeffitsienta v parabolicheskom uravnenii”, Differentsialnye uravneniya, 47:1 (2011), 92–102  mathscinet  zmath  elib
    18. Kamynin V.L., “Unique Solvability of the Inverse Problem of Determination of the Leading Coefficient in a Parabolic Equation”, Differ. Equ., 47:1 (2011), 91–101  crossref  mathscinet  zmath  isi  elib
    19. Guochun Wen, Dechang Chen, “Boundary Value Problems for Nonlinear Elliptic Equations of Second Order in High Dimensional Domains”, AM, 04:12 (2013), 1651  crossref  mathscinet
    20. Louanas Bouzidi, Arezki Kheloufi, “Global in time results for a parabolic equation solution in non-rectangular domains”, Zhurn. SFU. Ser. Matem. i fiz., 13:3 (2020), 257–274  mathnet  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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