The asymptotic properties of solutions to a multi-dimensional Newtonian filtration equations

Abstract

This paper deals with the exterior problem of the multidimensional Newtonian filtration equations coupled via nonlinear boundary flux. The asymptotic properties of solutions including the critical global existence curve and the critical Fujita curve are determined. In particular, an interesting phenomenon is shown, there exists a threshold value for the spacial dimension such that the critical global existence curve and the critical Fujita curve are the same when the spacial dimension , while these two critical curves are entirely different when .

Keywords:

• Newtonian polytropic equation
• global existence
• blow-up
• critical curve

AMS Subject Classifications:

• 35K65
• 35B33

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the NSFC of China [grant number 11461076],[grant number 61364020]; the Universities and Colleges Research Foundation of Guangxi [grant number ZD2014106].