Li, Yuxiang; Wu, Jichun Extinction for fast diffusion equations with nonlinear sources. (English) Zbl 1073.35134 Electron. J. Differ. Equ. 2005, Paper No. 23, 7 p. (2005). Summary: 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 \(\mathbb R^N\) 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. Cited in 14 Documents MSC: 35K65 Degenerate parabolic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35K55 Nonlinear parabolic equations Keywords:Extinction; fast diffusion; first eigenvalue PDFBibTeX XMLCite \textit{Y. Li} and \textit{J. Wu}, Electron. J. Differ. Equ. 2005, Paper No. 23, 7 p. (2005; Zbl 1073.35134) Full Text: EuDML EMIS