RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Ufimsk. Mat. Zh., 2013, Volume 5, Issue 1, Pages 63–82 (Mi ufa187)  

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

Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains

L. M. Kozhevnikova, A. A. Leontiev

Sterlitamak State Pedagogical Academy

Abstract: This work is devoted to a class of parabolic equations with double nonlinearity whose representative is a model equation
$$(|u|^{k-2}u)_t=\sum_{\alpha=1}^n(|u_{x_{\alpha}} |^{p_{\alpha}-2}u_{x_{\alpha}})_{x_\alpha},\quad p_n\geq \ldots \geq p_1>k,\quad k\in(1,2).$$
For the solution of the first mixed problem in a cylindrical domain $ D=(0,\infty)$ $\times\Omega, \;$ ${\Omega\subset \mathbb{R}_n,}$ $\;n\geq 2$ with homogeneous Dirichlet boundary condition and compactly supported initial function precise estimates the rate of decay as $t\rightarrow\infty$ are established. Earlier these results were obtained by the authors for $k\geq 2$. The case $k\in(1,2)$ differs by the method of constructing Galerkin's approximations that for an isotropic model equation was proposed by E. R. Andriyanova and F. Kh. Mukminov.

Keywords: anisotropic equation, doubly nonlinear parabolic equations, existence of strong solution, decay rate of solution.

Full text: PDF file (542 kB)
References: PDF file   HTML file

English version:
Ufa Mathematical Journal, 2013, 5:1, 63–82 (PDF, 448 kB); https://doi.org/10.13108/2013-5-1-63

Bibliographic databases:

UDC: 517.946
Received: 23.12.2011

Citation: L. M. Kozhevnikova, A. A. Leontiev, “Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains”, Ufimsk. Mat. Zh., 5:1 (2013), 63–82; Ufa Math. J., 5:1 (2013), 63–82

Citation in format AMSBIB
\Bibitem{KozLeo13}
\by L.~M.~Kozhevnikova, A.~A.~Leontiev
\paper Decay of solution of anisotropic doubly nonlinear parabolic equation in unbounded domains
\jour Ufimsk. Mat. Zh.
\yr 2013
\vol 5
\issue 1
\pages 63--82
\mathnet{http://mi.mathnet.ru/ufa187}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3429951}
\elib{http://elibrary.ru/item.asp?id=18929627}
\transl
\jour Ufa Math. J.
\yr 2013
\vol 5
\issue 1
\pages 63--82
\crossref{https://doi.org/10.13108/2013-5-1-63}


Linking options:
  • http://mi.mathnet.ru/eng/ufa187
  • http://mi.mathnet.ru/eng/ufa/v5/i1/p63

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, A. A. Leontev, “Resheniya anizotropnykh parabolicheskikh uravnenii s dvoinoi nelineinostyu v neogranichennykh oblastyakh”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 82–89  mathnet  crossref
    2. 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
    3. 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
    4. E. R. Andriyanova, F. Kh. Mukminov, “Existence of solution for parabolic equation with non-power nonlinearities”, Ufa Math. J., 6:4 (2014), 31–47  mathnet  crossref
    5. 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
    6. F. Kh. Mukminov, “Uniqueness of the renormalized solutions to the Cauchy problem for an anisotropic parabolic equation”, Ufa Math. J., 8:2 (2016), 44–57  mathnet  crossref  isi  elib
    7. F. Kh. Mukminov, “Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces”, Sb. Math., 208:8 (2017), 1187–1206  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • ”фимский математический журнал
    Number of views:
    This page:259
    Full text:88
    References:45
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019