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Existence and Non-existence of a Fast Diffusion Equation inRn

✍ Scribed by Yuan-Wei Qi

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 299 KB
Volume: 136
Category: Article
ISSN: 0022-0396
DOI: 10.1006/jdeq.1996.3246

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✦ Synopsis

In this paper we study the global existence and asymptotic behaviour of solutions to u t =2 log u for the Cauchy initial value problem in R n . We prove that if n 3, then every solution satisfies R n u p (x, t) dx= for any 1< p nÂ2, where 0nÂ2. Hence, we extend a previous result of Vazquez [19] which claims that R n u dx= for 0<t<t max .

1997 Academic Press

We assume that u 0 (x) is a continuous function.

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