Extinction for fast diffusion equations with nonlinear sources
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Date
2005-02-20
Authors
Li, Yuxiang
Wu, Jichun
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We establish conditions for the extinction of solutions, in finite time, of the fast diffusion problem ut = ∆um + λup, 0 < m < 1, in a bounded domain of RN 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.
Description
Keywords
Extinction, Fast diffusion, First eigenvalue
Citation
Li, Y., & Wu, J. (2005). Extinction for fast diffusion equations with nonlinear sources. <i>Electronic Journal of Differential Equations, 2005</i>(23), pp. 1-7.
Rights
Attribution 4.0 International