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Mat. Sb., 2004, Volume 195, Number 3, Pages 115–142 (Mi msb810)  

This article is cited in 12 scientific papers (total in 12 papers)

Stabilization of the norm of the solution of a mixed problem in an unbounded domain for parabolic equations of orders 4 and 6

F. Kh. Mukminov, I. M. Bikkulov

Sterlitamak State Pedagogical Institute

Abstract: The behaviour as $t\to\infty$ of the solution of a mixed problem for parabolic equations in an unbounded domain with two exits to infinity is studied. A certain class of domains is distinguished, in which an estimate characterizing the stabilization of solutions and determined by the geometry of the domain is established. This estimate is proved to be sharp in a certain sense for a broad class of domains with two exits to infinity.


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English version:
Sbornik: Mathematics, 2004, 195:3, 413–440

Bibliographic databases:

UDC: 517.956.4
MSC: 35K25, 35B40
Received: 21.07.2003

Citation: 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”, Mat. Sb., 195:3 (2004), 115–142; Sb. Math., 195:3 (2004), 413–440

Citation in format AMSBIB
\by F.~Kh.~Mukminov, I.~M.~Bikkulov
\paper Stabilization of the norm of the solution of a~mixed problem
in an~unbounded domain
for parabolic equations of~orders~4~and~6
\jour Mat. Sb.
\yr 2004
\vol 195
\issue 3
\pages 115--142
\jour Sb. Math.
\yr 2004
\vol 195
\issue 3
\pages 413--440

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    This publication is cited in the following articles:
    1. 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
    2. L. M. Kozhevnikova, F. Kh. Mukminov, “Decay of the solution of the first mixed problem for a high-order parabolic equation with minor terms”, J. Math. Sci., 150:5 (2008), 2369–2383  mathnet  crossref  mathscinet  zmath  elib
    3. I. M. Bikkulov, F. Kh. Mukminov, “Klassy edinstvennosti resheniya zadachi Rikke dlya ellipticheskikh uravnenii chetvertogo i shestogo poryadkov”, Ufimsk. matem. zhurn., 2:1 (2010), 35–51  mathnet  zmath  elib
    4. Gilimshina V.F., “On the decay of a solution of a nonuniformly parabolic equation”, Differential Equations, 46:2 (2010), 239–254  crossref  mathscinet  zmath  isi  elib
    5. 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
    6. V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56  mathnet  zmath
    7. L. M. Kozhevnikova, A. A. Leontev, “Otsenki resheniya anizotropnogo parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:4 (2011), 64–85  mathnet  zmath
    8. T. K. Yuldashev, “Obratnaya zadacha dlya nelineinogo integro-differentsialnogo uravneniya Fredgolma chetvertogo poryadka s vyrozhdennym yadrom”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:4 (2015), 736–749  mathnet  crossref  zmath  elib
    9. T. K. Yuldashev, “Obratnaya zadacha dlya odnogo nelineinogo uravneniya v chastnykh proizvodnykh vosmogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 136–154  mathnet  crossref  zmath  elib
    10. 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
    11. T. K. Yuldashev, “Inverse problem for a nonlinear Benney–Luke type integro-differential equations with degenerate kernel”, Russian Math. (Iz. VUZ), 60:9 (2016), 53–60  mathnet  crossref  isi
    12. T. K. Yuldashev, “Ustoichivost i differentsiruemost po malomu parametru smeshannoi zadachi dlya nelineinogo uravneniya v chastnykh proizvodnykh vosmogo poryadka”, Zhurnal SVMO, 18:1 (2016), 82–93  mathnet  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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