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Critical extinction exponents for a fast diffusion equation with nonlocal source and absorption

Haixia Li and Yuzhu Han*

Author Affiliations

Department of Mathematics, Jilin University, Changchun, 130012, P.R. China

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Boundary Value Problems 2014, 2014:24  doi:10.1186/1687-2770-2014-24

Published: 30 January 2014


In this article, the authors apply the super-solution and sub-solution methods, instead of energy estimate methods, to investigate the critical extinction exponents for a fast diffusion equation with a nonlocal source and an absorption term. They give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve, in some sense, the results by Xu et al. (Bound. Value Probl. 2013:24 2013) and by Han et al. (Arch. Math. 97:353-363, 2011).

MSC: 35K55, 35K57.

fast diffusion equation; critical exponents; extinction; super-solutions and sub-solutions