Blow-up for a double degenerate quasilinear parabolic equation

Abstract

Existence of a unique classical non-negative solution is established and the sufficient conditions for the solution that exists locally or blow-up in finite time are obtained for the double degenerate quasilinear parabolic equation with homogeneous Dirichlet boundary conditions. Furthermore, under certain conditions we obtain the estimates of blow-up rate of solution.

Keywords:

• double degenerate quasilinear parabolic system
• global existence
• blow-up
• blow-up rate

2000 AMS Subject Classifications: :

• 35K55
• 35K65

Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grant No. 10871060) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB110005).