Abstract:

This paper deals with the extinction properties of solutions to a class of fast diffusion equations coupled with localized sources. Analyzing the effect of the diffusion term and the source term on the extinction properties of solutions and constructing some proper sub and supersolutions, the authors obtained the critical extinction exponents of the problem. The results show that when the exponent of the source term is suitably large any solution of the problem vanishes in finite time for appropriately small initial data, while the maximal solution will not vanish at any finite time provided that the exponent of the source term is suitably small.

Key words: fast diffusion equation, localized source, critical extinction exponent