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Articles

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

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Pages 153-168 | Received 17 Dec 2012, Accepted 21 Jan 2014, Published online: 20 Feb 2014
 

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.

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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).

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