Blow-up for a degenerate parabolic equation with nonlocal source and nonlocal boundary

Abstract

In this article, we investigate the blow-up properties of the positive solutions for a doubly degenerate parabolic equation with nonlocal source and nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we give the precise blow-up rate estimate and the uniform blow-up estimate for the blow-up solution.

Keywords:

• degenerate parabolic equation
• blow-up
• nonlocal boundary
• blow-up rate
• uniform blow-up profile

AMS Subject Classifications::

• 35B35
• 35K60

Acknowledgements

The authors thank the anonymous referees for their careful reading and useful suggestions. This work is supported by NSF of China (11071266) and by NSF project of CQ CSTC (2010BB9218).