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Trudy Mat. Inst. Steklov., 1973, Volume 126, Pages 5–45 (Mi tm3138)  

This article is cited in 26 scientific papers (total in 26 papers)

The estimates of the solutions of boundary value problems for a second order parabolic equation

A. K. Gushchin


Full text: PDF file (3026 kB)

English version:
Proceedings of the Steklov Institute of Mathematics, 1973, 126, 1–46

Bibliographic databases:
UDC: 517.947.4

Citation: A. K. Gushchin, “The estimates of the solutions of boundary value problems for a second order parabolic equation”, Boundary value problems for differential equations. Part III, Trudy Mat. Inst. Steklov., 126, 1973, 5–45; Proc. Steklov Inst. Math., 126 (1973), 1–46

Citation in format AMSBIB
\Bibitem{Gus73}
\by A.~K.~Gushchin
\paper The estimates of the solutions of boundary value problems for a second order parabolic equation
\inbook Boundary value problems for differential equations. Part~III
\serial Trudy Mat. Inst. Steklov.
\yr 1973
\vol 126
\pages 5--45
\mathnet{http://mi.mathnet.ru/tm3138}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=336025}
\zmath{https://zbmath.org/?q=an:0288.35029}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1973
\vol 126
\pages 1--46


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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. A. K. Gushchin, “On an estimate of the Dirichlet integral in unbounded domains”, Math. USSR-Sb., 28:2 (1976), 249–261  mathnet  crossref  mathscinet  zmath  isi
    2. A. K. Gushchin, “Stabilization of the solutions of the second boundary value problem for a second order parabolic equation”, Math. USSR-Sb., 30:4 (1976), 403–440  mathnet  crossref  mathscinet  zmath  isi
    3. V. I. Ushakov, “Stabilization of solutions of the third mixed problem for a second order parabolic equation in a noncylindrical domain”, Math. USSR-Sb., 39:1 (1981), 87–105  mathnet  crossref  mathscinet  zmath  isi
    4. F. Kh. Mukminov, “Stabilization of solutions of the first mixed problem for a parabolic equation of second order”, Math. USSR-Sb., 39:4 (1981), 449–467  mathnet  crossref  mathscinet  zmath  isi
    5. A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498  mathnet  crossref  mathscinet  zmath
    6. A. I. Ibragimov, “Some qualitative properties of solutions of the mixed problem for equations of elliptic type”, Math. USSR-Sb., 50:1 (1985), 163–176  mathnet  crossref  mathscinet  zmath
    7. A. K. Gushchin, V. P. Mikhailov, Yu. A. Mikhailov, “On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation”, Math. USSR-Sb., 56:1 (1987), 141–162  mathnet  crossref  mathscinet  zmath
    8. A. V. Lezhnev, “On the behavior, for large time values, of nonnegative solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 57:1 (1987), 195–209  mathnet  crossref  mathscinet  zmath
    9. Yu. A. Mikhailov, “On uniform quasistabilization of solutions of the second mixed problem for a second-order hyperbolic equation”, Math. USSR-Sb., 57:1 (1987), 243–262  mathnet  crossref  mathscinet  zmath
    10. A. K. Gushchin, V. P. Mikhailov, “On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation”, Math. USSR-Sb., 59:2 (1988), 409–427  mathnet  crossref  mathscinet  zmath
    11. A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371  mathnet  crossref  mathscinet  zmath
    12. L. M. Kozhevnikova, F. Kh. Mukminov, “Estimates of the stabilization rate as $t\to\infty$ of solutions of the first mixed problem for a quasilinear system of second-order parabolic equations”, Sb. Math., 191:2 (2000), 235–273  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. F. Kh. Mukminov, I. M. Bikkulov, “Stabilization of the norm of the solution of a mixed problem in an unbounded domain for parabolic equations of orders 4 and 6”, Sb. Math., 195:3 (2004), 413–440  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. V. N. Denisov, “On the behaviour of solutions of parabolic equations for large values of time”, Russian Math. Surveys, 60:4 (2005), 721–790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. L. M. Kozhevnikova, “Stabilization of a solution of the first mixed problem for a quasi-elliptic evolution equation”, Sb. Math., 196:7 (2005), 999–1032  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. N. A. Kul'sarina, V. F. Gilimshina, “Exact estimate for the rate of decrease of a solution to a parabolic equation of the 2nd kind for $t\to\infty$”, Russian Math. (Iz. VUZ), 51:4 (2007), 32–41  mathnet  crossref  mathscinet  zmath
    17. V. I. Ushakov, O. V. Syrnikova, “On the Behavior of Large Values of the Time Required for Solving the Second Boundary-Value Problem for the Barenblatt–Zheltov–Kochina Equation in an Unbounded Domain”, Math. Notes, 86:2 (2009), 290–292  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. L. M. Kozhevnikova, “Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains”, Izv. Math., 74:2 (2010), 325–345  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. R. Kh. Karimov, L. M. Kozhevnikova, “Stabilization of solutions of quasilinear second order parabolic equations in domains with non-compact boundaries”, Sb. Math., 201:9 (2010), 1249–1271  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    20. V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56  mathnet  zmath
    21. L. M. Kozhevnikova, A. A. Leontev, “Otsenki resheniya anizotropnogo parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:4 (2011), 64–85  mathnet  zmath
    22. L. M. Kozhevnikova, F. Kh. Mukminov, “Stabilization of solutions of an anisotropic quasilinear parabolic equation in unbounded domains”, Proc. Steklov Inst. Math., 278 (2012), 106–120  mathnet  crossref  mathscinet  isi  elib  elib
    23. È. R. Andriyanova, F. Kh. Mukminov, “Stabilization of the solution of a doubly nonlinear parabolic equation”, Sb. Math., 204:9 (2013), 1239–1263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. E. R. Andriyanova, “Estimates of decay rate for solution to parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:2 (2014), 3–24  mathnet  crossref  elib
    25. 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
    26. V. F. Vil'danova, “On decay of solution to linear parabolic equation with double degeneracy”, Ufa Math. J., 8:1 (2016), 35–50  mathnet  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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