Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 23, pp. 1-7.

Title: Extinction for fast diffusion equations with 
       nonlinear sources

Authors: Yuxiang Li (Southeast Univ., Nanjing, China)
         Jichun Wu  (Nanjing Univ., Nanjing, China)
 
Abstract: 
 We establish conditions for the extinction of solutions,
 in finite time, of the fast diffusion problem
 $u_t=\Delta u^m+\lambda u^p$, $0<m<1$,
 in a bounded domain of $R^N$ with $N>2$.
 More precisely, we show that if $p>m$, the solution
 with small initial data vanishes in finite time,
 and if $p<m$,  the maximal solution is positive for all $t>0$.
 If $p=m$, then first eigenvalue of the Dirichlet problem plays
 a role.
 
Submitted September 15, 2004. Published February 20, 2005.
Math Subject Classifications: 35K20, 35K55.
Key Words: Extinction; fast diffusion; first eigenvalue.