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Izv. Akad. Nauk SSSR Ser. Mat., 1958, Volume 22, Issue 5, Pages 667–704 (Mi izv3993)  

This article is cited in 28 scientific papers (total in 28 papers)

The Cauchy problem and boundary problems for equations of the type of non-stationary filtration

O. A. Oleinik, A. S. Kalashnikov, Czou Juj-lin


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Received: 21.11.1957

Citation: O. A. Oleinik, A. S. Kalashnikov, Czou Juj-lin, “The Cauchy problem and boundary problems for equations of the type of non-stationary filtration”, Izv. Akad. Nauk SSSR Ser. Mat., 22:5 (1958), 667–704

Citation in format AMSBIB
\Bibitem{OleKalCzo58}
\by O.~A.~Oleinik, A.~S.~Kalashnikov, Czou Juj-lin
\paper The Cauchy problem and boundary problems for equations of the type of non-stationary filtration
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1958
\vol 22
\issue 5
\pages 667--704
\mathnet{http://mi.mathnet.ru/izv3993}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=99834}
\zmath{https://zbmath.org/?q=an:0093.10302}


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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. I. Vol'pert, S. I. Khudyaev, “Cauchy's problem for degenerate second order quasilinear parabolic equations”, Math. USSR-Sb., 7:3 (1969), 365–387  mathnet  crossref  mathscinet  zmath
    2. G. I. Barenblatt, Ya. B. Zel'dovich, “Intermediate asymptotics in matematical physics”, Russian Math. Surveys, 26:2 (1971), 45–61  mathnet  crossref  mathscinet  zmath
    3. A. S. Kalashnikov, “The concept of a finite rate of propagation of a perturbation”, Russian Math. Surveys, 34:2 (1979), 235–236  mathnet  crossref  mathscinet  zmath
    4. V. A. Galaktionov, A. A. Samarskii, “Methods of constructing approximate self-similar solutions of nonlinear heat equations. I”, Math. USSR-Sb., 46:3 (1983), 291–321  mathnet  crossref  mathscinet  zmath
    5. V. A. Galaktionov, A. A. Samarskii, “Methods of constructing approximate self-similar solutions of nonlinear heat equations. IV”, Math. USSR-Sb., 49:1 (1984), 125–149  mathnet  crossref  mathscinet  zmath
    6. A. S. Kalashnikov, “Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations”, Russian Math. Surveys, 42:2 (1987), 169–222  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. V. A. Galaktionov, “Accurate estimates for the amplitude and support of unbounded solutions of the nonlinear heat-conduction equation with a source”, U.S.S.R. Comput. Math. Math. Phys., 30:2 (1990), 67–74  mathnet  crossref  mathscinet  zmath
    8. Zh. N. Kudryasheva, “The solution of the problem of the motion of a conservative impurity in a river with a bed of arbitrary configuration”, Comput. Math. Math. Phys., 33:7 (1993), 929–938  mathnet  mathscinet  zmath  isi
    9. Comput. Math. Math. Phys., 33:2 (1993), 217–227  mathnet  mathscinet  zmath  isi
    10. A. E. Shishkov, “Propagation of perturbation in a singular Cauchy problem for degenerate quasilinear parabolic equations”, Sb. Math., 187:9 (1996), 1391–1410  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. A. S. Kalashnikov, “Discretization and nonlinear effects in mathematical models of heat conduction theory”, Comput. Math. Math. Phys., 38:4 (1998), 578–584  mathnet  mathscinet  zmath
    12. A. E. Shishkov, A. G. Shchelkov, “Blow-up boundary regimes for general quasilinear parabolic equations in multidimensional domains”, Sb. Math., 190:3 (1999), 447–479  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. A. E. El'bert, “Asymptotics of solutions to a nonlinear parabolic equation in the neighborhood of front formation”, Comput. Math. Math. Phys., 41:10 (2001), 1455–1469  mathnet  mathscinet  zmath  elib
    14. A. E. Shishkov, “Localized Boundary Blow-up Regimes for General Quasilinear Divergent Parabolic Equations of Arbitrary Order”, Proc. Steklov Inst. Math., 236 (2002), 341–356  mathnet  mathscinet  zmath
    15. S. P. Bautin, “Suschestvovanie analiticheskoi teplovoi volny, opredelyaemoi zadannym kraevym rezhimom”, Sib. zhurn. industr. matem., 6:1 (2003), 3–11  mathnet  mathscinet  zmath
    16. N. A. Vaganova, “Constructing new classes of solutions of a nonlinear filtration equation by special consistent series”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 2, S182–S193  mathnet  mathscinet  zmath  elib
    17. O. O. Kovrizhnykh, “On the construction of an asymptotic solution of a nonlinear degenerate parabolic equation”, Comput. Math. Math. Phys., 43:10 (2003), 1430–1436  mathnet  mathscinet  zmath  elib
    18. G. A. Rudykh, A. V. Sinitsyn, “Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations”, Math. Notes, 77:2 (2005), 199–212  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. D. A. Sapronov, A. E. Shishkov, “Asymptotic behaviour of supports of solutions of quasilinear many-dimensionsal parabolic equations of non-stationary diffusion-convection type”, Sb. Math., 197:5 (2006), 753–790  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. St. Petersburg Math. J., 19:2 (2008), 239–251  mathnet  crossref  mathscinet  zmath  isi  elib
    21. G. A. Rudykh, “Analiz statsionarnykh reshenii nachalno-kraevoi zadachi dlya nelokalnogo parabolicheskogo uravneniya fiziki plazmy”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 3:2 (2010), 61–87  mathnet
    22. A. L. Kazakov, “Primenenie kharakteristicheskikh ryadov dlya postroeniya reshenii nelineinykh parabolicheskikh uravnenii i sistem s vyrozhdeniem”, Tr. IMM UrO RAN, 18, no. 2, 2012, 114–122  mathnet  elib
    23. A. L. Kazakov, L. F. Spevak, “Metody granichnykh elementov i stepennykh ryadov v odnomernykh zadachakh nelineinoi filtratsii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:2 (2012), 2–17  mathnet
    24. P. A. Kuznetsov, “O kraevoi zadache s vyrozhdeniem dlya nelineinogo uravneniya teploprovodnosti s dannymi na zamknutoi poverkhnosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 9 (2014), 61–74  mathnet
    25. A. L. Kazakov, P. A. Kuznetsov, A. A. Lempert, “O postroenii teplovoi volny dlya nelineinogo uravneniya teploprovodnosti v simmetrichnom sluchae”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 11 (2015), 39–53  mathnet
    26. G. A. Rudykh, E. I. Semenov, “Issledovanie sovmestnosti pereopredelennoi sistemy dlya mnogomernogo uravneniya nelineinoi teploprovodnosti (chastnyi sluchai)”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 18 (2016), 93–109  mathnet
    27. V. B. Bednova, “Ob odnom metode priblizhennogo resheniya nelineinogo uravneniya teploprovodnosti”, Chebyshevskii sb., 17:4 (2016), 11–22  mathnet  crossref  elib
    28. G. A. Rudykh, E. I. Semenov, “Issledovanie sovmestnosti pereopredelennoi sistemy dlya mnogomernogo uravneniya nelineinoi teploprovodnosti”, Matematicheskie zametki SVFU, 25:1 (2018), 50–62  mathnet  crossref  elib
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