Non-simultaneous blow-up in localized reaction–diffusion equations

Abstract

This article deals with blow-up solutions in reaction–diffusion equations coupled via localized exponential sources, subject to null Dirichlet conditions. The optimal and complete classification is obtained for simultaneous and non-simultaneous blow-up solutions. Moreover, blow-up rates and blow-up sets are also discussed. It is interesting that, in some exponent regions, blow-up phenomena depend sensitively on the choosing of initial data, and the localized nonlinearities play important roles in the blow-up properties of solutions.

Keywords:

• simultaneous blow-up
• non-simultaneous blow-up
• blow-up rate
• blow-up set

AMS Subject Classifications:

• Primary 35K05
• 35K60
• 35B40
• 35B33

Acknowledgements

This work is supported by the Shandong Provincial Natural Science Foundation, China (ZR2009AQ016) and the Fundamental Research Funds for the Central Universities (09CX05004A).