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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 2, Pages 109–130 (Mi izv2783)  

This article is cited in 9 scientific papers (total in 9 papers)

Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains

L. M. Kozhevnikovaab

a Sterlitamak State Pedagogical Academy
b Sterlitamak Branch of Academy of Sciences of Bashkortostan

Abstract: We consider the first mixed problem in a cylindrical domain $D=(0,\infty)\times\Omega$ for a pseudo-differential parabolic equation with homogeneous Dirichlet boundary conditions and a finitely supported initial function. We find upper bounds for the $L_2$-norm of a solution as $t\to\infty$ in terms of a geometric characteristic introduced earlier by the author for an unbounded domain $\Omega\subset\mathbb R^n$, $n\ge 2$, in the case of a higher-order parabolic equation.

Keywords: stabilization of solutions, pseudo-differential parabolic equations, unbounded domain, mixed problem.

DOI: https://doi.org/10.4213/im2783

Full text: PDF file (650 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:2, 325–345

Bibliographic databases:

UDC: 517.956.4
MSC: 35B35, 35B40, 35B45, 35H30, 35K20, 35K35, 74G30, 74H25
Received: 30.03.2008
Revised: 10.09.2008

Citation: L. M. Kozhevnikova, “Stabilization of solutions of pseudo-differential parabolic equations in unbounded domains”, Izv. RAN. Ser. Mat., 74:2 (2010), 109–130; Izv. Math., 74:2 (2010), 325–345

Citation in format AMSBIB
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  • https://doi.org/10.4213/im2783
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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. 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
    2. E. R. Andriyanova, F. Kh. Mukminov, “Otsenka snizu skorosti ubyvaniya resheniya parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:3 (2011), 3–14  mathnet  mathscinet  zmath
    3. V. F. Gilimshina, F. Kh. Mukminov, “Ob ubyvanii resheniya vyrozhdayuschegosya lineinogo parabolicheskogo uravneniya”, Ufimsk. matem. zhurn., 3:4 (2011), 43–56  mathnet  zmath
    4. L. M. Kozhevnikova, A. A. Leontev, “Otsenki resheniya anizotropnogo parabolicheskogo uravneniya s dvoinoi nelineinostyu”, Ufimsk. matem. zhurn., 3:4 (2011), 64–85  mathnet  zmath
    5. 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
    6. L. M. Kozhevnikova, A. A. Leont'ev, “Solutions to higher-order anisotropic parabolic equations in unbounded domains”, Sb. Math., 205:1 (2014), 7–44  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. È. R. Andriyanova, F. Kh. Mukminov, “Existence and qualitative properties of a solution of the first mixed problem for a parabolic equation with non-power-law double nonlinearity”, Sb. Math., 207:1 (2016), 1–40  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. V. F. Vil'danova, “Existence and uniqueness of a weak solution of a nonlocal aggregation equation with degenerate diffusion of general form”, Sb. Math., 209:2 (2018), 206–221  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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