Note on nonsimultaneous blow-up of n components for nonlinear parabolic systems

Abstract

This paper deals with the nonsimultaneous blow-up problems for with coupled nonlinear boundary flux . The main results extend the existence of two components blowing up simultaneously in the paper J. Math. Anal. Appl. 2009;356:215–231 to the case of components blowing up simultaneously. We verify that blow-up phenomena are independent of the choosing of the initial data in some exponent regions, while, in some others, the blow-up phenomena depend sensitively on the choosing of initial data. Moreover, the blow-up rates and sets are obtained for blow-up components.

Keywords:

• nonsimultaneous blow-up
• n components
• blow-up rate
• blow-up set

AMS Subject Classifications:

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

Notes

1 This paper is partially supported by National Natural Science Foundation of China [grant number 11201483], Shandong Provincial Natural Science Foundation, China, and the Fundamental Research Funds for the Central Universities.