Global existence and blow-up for weakly coupled degenerate and singular parabolic equations with nonlocal source

Abstract

This paper deals with the following weakly coupled degenerate and singular parabolic equations with nonlocal sourcein , where , be constants and are positive real numbers and . The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution that exist globally or blows up in finite time are obtained. Furthermore, under certain conditions, it is proved that the blow-up set of the blowing-up solution is any closed subset of the interval . Furthermore, we also obtain the blow-up rate under the condition .

Keywords:

• degenerate and singular parabolic equations
• nonlocal source
• global existence
• blow-up

AMS Subject Classifications:

• 35K55
• 35K57
• 35K65

Notes

1 The second author is supported by the Scientific Research Found of Sichuan Provincial Education Department (No.12ZA288), and the third author is supported in part by NSF of China (11071266) and in part by Natural Science Foundation Project of CQ CSTC (2010BB9218).