2014/07/10 by Hui, Kin Ming · 1 citation
#35K65 Secondary 35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35B40
paper · doi:10.48550/arxiv.1407.2696
Let n≥ 3, 00, β≥(mρ1)/(n-2-nm) and α=(2β+ρ1)/(1-m). For any λ>0, we will prove the existence and uniqueness (for β≥(ρ1)/(n-2-nm)) of radially symmetric singular solution gλ∈ C∞(Rn∖\0\) of the elliptic equation Δvm+αv+βx⋅∇ v=0, v>0, in Rn∖\0\, satisfying lim|x|→ 0|x|α/βgλ(x)=λ-(ρ1)/((1-m)β). When β is sufficiently large, we prove the higher order asymptotic behaviour of radially symmetric solutions of the above elliptic equation as |x|→∞. We also obtain an inversion formula for the radially symmetric solution of the above equation. As a consequence we will prove the extinction behaviour of the solution u of the fast diffusion equation ut=Δum in Rn× (0,T) near the extinction time T>0.