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 Ufimsk. Mat. Zh., 2011, Volume 3, Issue 4, Pages 43–56 (Mi ufa117)

On decay rate of solution to degenerating linear parabolic equations

V. F. Gilimshinaa, F. Kh. Mukminovb

a Bashkir State Pedagogical University, Ufa, Russia
b Ufa State Aviation Technical University, Ufa, Russia

Abstract: Existence and uniqueness of the solution to a linear degenerating parabolic equation is established in unbounded domains by the method of Galerkin's approximations. The first and the third boundary-value conditions are considered. The upper estimate of the solution decay rate is established when $x\to\infty$ in view of the influence of higher-order coefficients of the equation. The upper estimate of the decay rate of the solution $t\to\infty$ depending on the geometry of the unbounded domain is proved as well.

Keywords: degenerating parabolic equation, decay rate of solution, upper estimates, existence of solution.

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Document Type: Article
UDC: 517.946

Citation: V. F. Gilimshina, F. Kh. Mukminov, “On decay rate of solution to degenerating linear parabolic equations”, Ufimsk. Mat. Zh., 3:4 (2011), 43–56

Citation in format AMSBIB
\Bibitem{GilMuk11} \by V.~F.~Gilimshina, F.~Kh.~Mukminov \paper On decay rate of solution to degenerating linear parabolic equations \jour Ufimsk. Mat. Zh. \yr 2011 \vol 3 \issue 4 \pages 43--56 \mathnet{http://mi.mathnet.ru/ufa117} \zmath{https://zbmath.org/?q=an:1249.35132} 

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This publication is cited in the following articles:
1. V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597
2. 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
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