Dead-core rate for the fast diffusion equation with strong absorption in higher dimensional cases

Pan Zheng, Chunlai Mu and Xuegang Hu

Applied Mathematics and Computation, 2018, vol. 335, issue C, 292-304

Abstract: This paper deals with the dead-core rate for the fast diffusion equation with a strong absorption in several space dimensions ut=Δum−up,(x,t)∈Ω×(0,∞),where 0 < p < m < 1 and Ω=B(0,1)={x∈RN:|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 −up is replaced by −a(x,t)up, 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.

Keywords: Fast diffusion equation; Strong absorption; Dead-core rate (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:335:y:2018:i:c:p:292-304

DOI: 10.1016/j.amc.2018.04.016

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