Extinction and non-extinction profiles for the sub-critical fast diffusion equation with weighted source

2023/02/19 by Iagar, Razvan Gabriel, Muñoz, Ana Isabel, Sánchez, Ariel · 2 citations
#35B33 #35B36 #35C06 #35K57 #35K59 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.09641

Abstract

We establish both extinction and non-extinction self-similar profiles for the following fast diffusion equation with a weighted source term ∂_tu=Δu^m+|x|^σu^p, posed for (x,t)∈\real^N×(0,∞), N≥3, in the sub-critical range of the fast diffusion equation 00 and max\p_c(σ),1\0, in the form u(x,t)=t^αf(|x|t^β), f(ξ)∼ Cξ^-(N-2)/m, αgt;0, βgt;0 exist, provided 0

Cited by

• Self-similar blow-up solutions for the supercritical parabolic Hardy-Hénon equation
• Sharp non-existence threshold for a parabolic Hardy-Hénon equation with quasilinear diffusion

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