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- W2804076165 abstract "Abstract This paper deals with the dead-core rate for the fast diffusion equation with a strong absorption in several space dimensions u t = Δ u m − u p , ( x , t ) ∈ Ω × ( 0 , ∞ ) , where 0 Ω = B ( 0 , 1 ) = { x ∈ R N : | x | 1 } with N ≥ 1. By using the self-similar transformation technique and the Zelenyak method, in higher dimensional radially symmetric cases, we prove that the dead-core rate is not self-similar. Moreover, we also give the precise estimates on the single-point final dead-core profile. Finally, when the absorption term − u p is replaced by − a ( x , t ) u p , then we derive that the dead-core rate can turn into the corresponding ODE rate if the coefficient function a(x, t) is a suitable uniformly bounded positive function, which implies that a(x, t) plays an important role in the study of the dead-core rate. The main aim of this paper is to extend the results obtained by Guo et al. (2010) to the higher dimensional radially symmetric case." @default.
- W2804076165 created "2018-06-01" @default.
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- W2804076165 date "2018-10-01" @default.
- W2804076165 modified "2023-10-17" @default.
- W2804076165 title "Dead-core rate for the fast diffusion equation with strong absorption in higher dimensional cases" @default.
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- W2804076165 doi "https://doi.org/10.1016/j.amc.2018.04.016" @default.
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