Global behaviour of solutions of the fast diffusion equation

2017/10/17 by Hsu, Shu-Yu
#35B09 (Secondary) #35B20 #35B40 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.06108

Abstract

We will extend a recent result of B.~Choi and P.~Daskalopoulos (\citeCD). For any n≥ 3, 00 and λ>0, we prove the higher order expansion of the radially symmetric solution v_λ,β(r) of (n-1)/(m)Δv^m+(2β)/(1-m) v+βx⋅∇ v=0 in ℝⁿ, v(0)=λ, as r→∞. As a consequence for any n≥ 3 and 00 and K₁∈ℝ, then as t→∞ the rescaled function \widetildeu(x,t)=e^(2β)/(1-m)tu(e^βtx,t) converges uniformly on every compact subsets of ℝⁿ to v_λ1,β for some constant λ₁>0.

Related

• Asymptotic large time behavior of singular solutions of the fast diffusion equation
• Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time
• Existence and asymptotic behaviour of solutions of the very fast diffusion equation
• Super fast vanishing solutions of the fast diffusion equation
• Large time behaviour of higher dimensional logarithmic diffusion equation