| Popis: |
We study the asymptotic large time behavior of singular solutions of the fast diffusion equation $u_t=\Delta u^m$ in $({\mathbb R}^n\setminus\{0\})\times(0,\infty)$ in the subcritical case $0A_1>0$ and $\frac{2}{1-m}<\gamma<\frac{n-2}{m}$, where $\beta:=\frac{1}{2-\gamma(1-m)}$, $\alpha:=\frac{2\beta-1}{1-m},$ and the self-similar profile $f_i$ satisfies the elliptic equation $$ \Delta f^m+\alpha f+\beta x\cdot \nabla f=0\quad \mbox{in ${\mathbb R}^n\setminus\{0\}$} $$ with $\lim_{|x|\to0}|x|^{\frac{ \alpha}{ \beta}}f_i(x)=A_i$ and $\lim_{|x|\to\infty}|x|^{\frac{n-2}{m}}{f_i}(x)= D_{A_i} $ for some constants $D_{A_i}>0$. When $\frac{2}{1-m}<\gammaComment: 37 pages |
