Global blow-up for a localized quasilinear parabolic system with nonlocal boundary conditions

Abstract

In this article, we investigate the positive solution of a localized quasilinear parabolic system with nonlocal boundary conditions. Under certain conditions, the global existence and finite time blow-up criteria are established, and the global blow-up behaviour is also obtained.

Keywords:

• nonlinear parabolic system
• localized reaction source
• nonlocal boundary condition
• global existence
• global blowup

AMS Subject Classifications::

• 35A01
• 35K20
• 35K57
• 35K59

Acknowledgements

The author thanks the anonymous referees for their careful reading and valuable suggestions which have improved the quality of this work. This research is supported by the research scheme of the Natural Science of the Universities of Jiangsu Province of China (08KJD110017).