ﻻ يوجد ملخص باللغة العربية
Let $nge 3$, $0<m<frac{n-2}{n}$, $rho_1>0$, $betagefrac{mrho_1}{n-2-nm}$ and $alpha=frac{2beta+rho_1}{1-m}$. For any $lambda>0$, we will prove the existence and uniqueness (for $betagefrac{rho_1}{n-2-nm}$) of radially symmetric singular solution $g_{lambda}in C^{infty}(R^nsetminus{0})$ of the elliptic equation $Delta v^m+alpha v+beta xcdot abla v=0$, $v>0$, in $R^nsetminus{0}$, satisfying $displaystylelim_{|x|to 0}|x|^{alpha/beta}g_{lambda}(x)=lambda^{-frac{rho_1}{(1-m)beta}}$. When $beta$ is sufficiently large, we prove the higher order asymptotic behaviour of radially symmetric solutions of the above elliptic equation as $|x|toinfty$. 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 $u_t=Delta u^m$ in $R^ntimes (0,T)$ near the extinction time $T>0$.
We study the asymptotic large time behavior of singular solutions of the fast diffusion equation $u_t=Delta u^m$ in $({mathbb R}^nsetminus{0})times(0,infty)$ in the subcritical case $0<m<frac{n-2}{n}$, $nge3$. Firstly, we prove the existence of singu
Let $OmegasubsetR^n$ be a smooth bounded domain and let $a_1,a_2,dots,a_{i_0}inOmega$, $widehat{Omega}=Omegasetminus{a_1,a_2,dots,a_{i_0}}$ and $widehat{R^n}=R^nsetminus{a_1,a_2,dots,a_{i_0}}$. We prove the existence of solution $u$ of the fast diffu
Let $nge 3$ and $0<m<frac{n-2}{n}$. We will extend the results of J.L. Vazquez and M. Winkler and prove the uniqueness of finite points blow-up solutions of the fast diffusion equation $u_t=Delta u^m$ in both bounded domains and $mathbb{R}^ntimes (0,
Let $ngeq 3$, $0< m<frac{n-2}{n}$ and $T>0$. We construct positive solutions to the fast diffusion equation $u_t=Delta u^m$ in $mathbb{R}^ntimes(0,T)$, which vanish at time $T$. By introducing a scaling parameter $beta$ inspired by cite{DKS}, we stud
For $nge 3$, $0<m<frac{n-2}{n}$, $beta<0$ and $alpha=frac{2beta}{1-m}$, we prove the existence, uniqueness and asymptotics near the origin of the singular eternal self-similar solutions of the fast diffusion equation in $(mathbb{R}^nsetminus{0})times