Lifespan and a new critical exponent for a nonlocal parabolic equation with slowly decay initial values

Abstract

In this paper, we consider the positive solution of the Cauchy problem for the following nonlocal parabolic equation

and give a new critical exponent for the existence of global and non-global solutions of the Cauchy problem. Furthermore, lifespan of the solutions is also studied.

Keywords:

• blow-up
• lifespan
• global existence
• critical exponent
• nonlocal parabolic equation
• slowly decay initial data

Classification:

• 35K55
• 35K57

View correction statement:

Erratum

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable suggestions and fruitful comments which significantly improved this work. The first author is supported in part by NSF of China (11001189), the second author is supported in part by NSF of China (11071226) and in part by Natural Science Foundation Project of CQ CSTC(2010BB9218).