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International Journal of Differential Equations
Volume 2012 (2012), Article ID 417261, 16 pages
http://dx.doi.org/10.1155/2012/417261
Review Article

Life Span of Positive Solutions for the Cauchy Problem for the Parabolic Equations

Department of Applied Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Received 15 December 2011; Accepted 30 January 2012

Academic Editor: Ebrahim Momoniat

Copyright © 2012 Yusuke Yamauchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Since 1960's, the blow-up phenomena for the Fujita type parabolic equation have been investigated by many researchers. In this survey paper, we discuss various results on the life span of positive solutions for several superlinear parabolic problems. In the last section, we introduce a recent result by the author.