Gilimshina, V. F.; Mukminov, F. Kh. On decay rate of solution to degenerating linear parabolic equation. (Russian. English summary) Zbl 1249.35132 Ufim. Mat. Zh. 3, No. 4, 43-56 (2011). Summary: 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 \(x\rightarrow\infty\) in view of the influence of higher-order coefficients of the equation. The upper estimate of the decay rate of the solution \(t\rightarrow\infty\) depending on the geometry of the unbounded domain is proved as well. Reviewer: Svetlana A. Grishina (Ul’yanovsk) MSC: 35K10 Second-order parabolic equations Keywords:degenerate parabolic equation; solution decay rate; upper estimates; solution existence PDFBibTeX XMLCite \textit{V. F. Gilimshina} and \textit{F. Kh. Mukminov}, Ufim. Mat. Zh. 3, No. 4, 43--56 (2011; Zbl 1249.35132) Full Text: MNR