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On decay rate of solution to degenerating linear parabolic equation. (Russian. English summary) Zbl 1249.35132

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.

MSC:

35K10 Second-order parabolic equations
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