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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 3, Pages 51–66 (Mi izv335)  

This article is cited in 7 scientific papers (total in 7 papers)

On uniqueness classes of solutions of the first mixed problem for a quasi-linear second-order parabolic system in an unbounded domain

L. M. Kozhevnikova

Sterlitamak State Pedagogical Institute

Abstract: We study a quasi-linear parabolic system of divergence type having an energy inequality and satisfying monotonicity conditions. For such a system, the first mixed problem is considered in a cylindrical domain $\{t>0\}\times\Omega$ that is unbounded with respect to the spatial variables. Generally, the initial vector function $\varphi$ in the problem may not belong to $\mathbb L_2(\Omega)$. A uniqueness class close to that of Täcklind [3] is established for the solutions of this problem. Moreover, a uniqueness theorem is proved for a solution belonging to this class and having an initial vector function increasing at infinity.

DOI: https://doi.org/10.4213/im335

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English version:
Izvestiya: Mathematics, 2001, 65:3, 469–484

Bibliographic databases:

MSC: 35A05, 35B45, 35K15, 35K30, 35K50, 35K65
Received: 15.07.1999

Citation: L. M. Kozhevnikova, “On uniqueness classes of solutions of the first mixed problem for a quasi-linear second-order parabolic system in an unbounded domain”, Izv. RAN. Ser. Mat., 65:3 (2001), 51–66; Izv. Math., 65:3 (2001), 469–484

Citation in format AMSBIB
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\by L.~M.~Kozhevnikova
\paper On uniqueness classes of solutions of the first mixed problem for a~quasi-linear second-order parabolic system in an unbounded domain
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 3
\pages 51--66
\mathnet{http://mi.mathnet.ru/izv335}
\crossref{https://doi.org/10.4213/im335}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1853365}
\zmath{https://zbmath.org/?q=an:0996.35028}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 469--484
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000335}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746819276}


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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. L. M. Kozhevnikova, “Uniqueness classes for solutions in unbounded domains of the first mixed problem for the equation $u_t=Au$ with quasi-elliptic operator $A$”, Sb. Math., 198:1 (2007), 55–96  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56  mathnet  zmath
    3. V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Muvasharkhan he Jenaliyev, Meiramkul Amangaliyeva, Minzilya Kosmakova, Murat Ramazanov, “About Dirichlet boundary value problem for the heat equation in the infinite angular domain”, Bound Value Probl, 2014:1 (2014)  crossref  mathscinet  zmath  scopus
    5. V. F. Vil'danova, F. Kh. Mukminov, “Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds”, Ufa Math. J., 7:2 (2015), 55–63  mathnet  crossref  isi  elib
    6. M. M. Amangalieva, M. T. Dzhenaliev, M. T. Kosmakova, M. I. Ramazanov, “On one homogeneous problem for the heat equation in an infinite angular domain”, Siberian Math. J., 56:6 (2015), 982–995  mathnet  crossref  crossref  mathscinet  isi  elib
    7. 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  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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