This article is cited in 2 scientific papers (total in 2 papers)
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
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.
degenerating parabolic equation, decay rate of solution, upper estimates, existence of solution.
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V. F. Gilimshina, F. Kh. Mukminov, “On decay rate of solution to degenerating linear parabolic equations”, Ufimsk. Mat. Zh., 3:4 (2011), 43–56
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\by V.~F.~Gilimshina, F.~Kh.~Mukminov
\paper On decay rate of solution to degenerating linear parabolic equations
\jour Ufimsk. Mat. Zh.
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V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597
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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