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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, Issue 1(30), Pages 82–89 (Mi vsgtu1186)  

This article is cited in 3 scientific papers (total in 3 papers)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains

L. M. Kozhevnikova, A. A. Leont'ev

Sterlitamak Branch of Bashkir State University, Sterlitamak, 453103, Russia

Abstract: This work is devoted to some class of parabolic equations of high order with double nonlinearity which can be represented by a model equation
\begin{gather*} \frac{\partial}{\partial t}(|u|^{k-2}u)= \sum_{\alpha=1}^n(-1)^{m_\alpha-1}\frac{\partial^{m_\alpha}}{\partial x_\alpha^{m_\alpha}} [|\frac{\partial^{m_\alpha} u}{\partial x_\alpha^{m_\alpha}}|^{p_\alpha-2} \frac{\partial^{m_\alpha} u}{\partial x_\alpha^{m_\alpha}}],m_1,\ldots, m_n\in \mathbb{N},\quad p_n\geq \ldots \geq p_1>k,\quad k>1. \end{gather*}
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 finite initial function the highest rate of decay established as $t \to \infty$. Earlier upper estimates were obtained by the authors for anisotropic equation of the second order and prove their accuracy.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-0081


DOI: https://doi.org/10.14498/vsgtu1186

Full text: PDF file (178 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.957
MSC: 35K35, 35K61
Original article submitted 15/XI/2012
revision submitted – 10/III/2013

Citation: L. M. Kozhevnikova, A. A. Leont'ev, “Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 82–89

Citation in format AMSBIB
\Bibitem{KozLeo13}
\by L.~M.~Kozhevnikova, A.~A.~Leont'ev
\paper Solutions of anisotropic parabolic equations with double non-linearity in unbounded domains
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 82--89
\mathnet{http://mi.mathnet.ru/vsgtu1186}
\crossref{https://doi.org/10.14498/vsgtu1186}


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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. 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
    2. 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
    3. 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
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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