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Ufimsk. Mat. Zh., 2016, Volume 8, Issue 1, Pages 38–53 (Mi ufa321)  

On decay of solution to linear parabolic equation with double degeneracy

V. F. Vil'danova

Bashkir State Pedagogical University named after M. Akhmulla, October rev. str., 3a, 450000, Ufa, Russia

Abstract: We obtain the upper bound for the decay rate of the solution to the Dirichlet initial boundary value problem for a linear parabolic second order equation with a double degeneracy $\mu(x)u_t=(\rho(x)a_{ij}(t,x)u_{x_i})_{x_j}$ in an unbounded domain. For a wide class of revolution domains we prove a lower bound. We adduce the examples showing that the upper and lower bounds are in some sense sharp.
We prove the unique solvability of the problem in an unbounded domain by Galerkin's approximations method.

Keywords: parabolic equation with a double degeneracy, decay rate of a solution, upper bound, existence of a solution.

Funding Agency Grant Number
M. Akmullah Bashkir State Pedagogical University
The work is supported by the grant for young scientists of the Scientific council of BSPU named after M. Akhmulla.


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English version:
Ufa Mathematical Journal, 2016, 8:1, 35–50

Document Type: Article
UDC: 517.946
MSC: 35B30, 35B45,35K10, 35K20, 35K65
Received: 25.10.2015

Citation: V. F. Vil'danova, “On decay of solution to linear parabolic equation with double degeneracy”, Ufimsk. Mat. Zh., 8:1 (2016), 38–53; Ufa Math. J., 8:1 (2016), 35–50

Citation in format AMSBIB
\Bibitem{Vil16}
\by V.~F.~Vil'danova
\paper On decay of solution to linear parabolic equation with double degeneracy
\jour Ufimsk. Mat. Zh.
\yr 2016
\vol 8
\issue 1
\pages 38--53
\mathnet{http://mi.mathnet.ru/ufa321}
\elib{http://elibrary.ru/item.asp?id=25631802}
\transl
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 1
\pages 35--50
\crossref{https://doi.org/10.13108/2016-8-1-35}


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