Growth estimates and blow-up in quasilinear parabolic problems

Abstract

Growth estimate of positive solution for a quasilinear parabolic equation subject to Robin boundary condition is presented by the maximum principles. The growth estimate is then used to study blow-up of the solution of the problem. The bounds of ‘blow-up time’ and blow-up rate are obtained.

Keywords:

• Quasilinear parabolic equation
• Growth estimate
• Blow-up
• Maximum principle

Keywords:

• 2000 Mathematics Subject Classifications: 35k55
• 35k60
• 35b45

Acknowledgments

The authors would like to thank Professor C.V. Pao for his helpful discussion. This work is supported by the National Natural Science Foundation of China (10372054, 70431002) and the Natural Science Foundation of Shanxi Province of China (20051004).