Secondary critical exponent and life span for a nonlocal parabolic p-Laplace equation

Abstract

This paper deals with positive solutions of the Cauchy problem for a parabolic p-Laplace equation with weighted nonlocal sources

where , , q, , , and . We classify global and non-global solutions of the Cauchy problem in the coexistence region by seeking a second critical exponent via the slow decay asymptotic behavior of an initial data at spatial infinity. Moreover, the large time behavior of global solution and the life span of non-global solution are derived.

Keywords:

• Parabolic p-Laplace equation
• weighted nonlocal sources
• secondary critical exponent
• large time behavior
• life span

AMS Subject Classifications:

• 35K65
• 35B33
• 35B40

Acknowledgements

The authors would like to deeply thank all the reviewers for their insightful and constructive comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Nature Science Foundation of China [grant number 11671188].