Cauchy problem for the non-Newtonian polytropic filtration equation with a localized reaction

Abstract

This paper is concerned with the Cauchy problem for the non-Newtonian polytropic filtration equation with a localized reactionwhere , , and is a compactly supported function. By constructing various self-similar super- and subsolutions, we give the critical global existence exponent and critical Fujita exponent . Moreover, under some suitable conditions, we obtain the results of blow-up rate and blow-up set for the non-global solution.

Keywords:

• critical exponent
• non-Newtonian polytropic filtration equation
• localized reaction
• global existence
• blow-up

AMS Subject Classifications:

• 35K55
• 35K65
• 35B40

Acknowledgments

The authors would like to express sincere gratitude to the referees for their valuable suggestions and comments on the original manuscript.

Notes

The work is supported in part by NSF of China(11371384) and in part by Natural Science Foundation Project of CQ CSTC(2010BB9218).