Tohoku Mathematical Journal
2001
December
SECOND SERIES VOL. 53, NO. 4

Tohoku Math. J.
53 (2001), 571-579

Title ON A FAST DIFFUSION EQUATION WITH SOURCE

Author Jong-Shenq Guo and Yung-Jen L. Guo

(Received January 19, 2000, revised December 4, 2000)
Abstract. We study in this paper the positive solution of the Cauchy problem for a fast diffusion equation with source. We derive a secondary critical exponent of the behavior of the initial value at infinity for the existence of global (in time) and nonglobal solutions of the Cauchy problem. Furthermore, the large time behaviors of those global solutions are also studied.

2000 Mathematics Subject Classification. Primary 35K55; Secondary 35K57, 34B15.
Key words and phrases. Fast diffusion equation, source, critical exponent.

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