Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2008-02-01

Journal: FRONTIERS OF MATHEMATICS IN CHINA

Included Journals: SCIE

Volume: 3

Issue: 1

Page Number: 87-99

ISSN: 1673-3452

Key Words: Parabolic equation; nonlinear absorption; nonlinear boundary flux; multiple blow-up rate; asymptotic analysis; characteristic algebraic system

Abstract: This paper deals with asymptotic analysis of a parabolic system with inner absorptions and coupled nonlinear boundary fluxes. Three simultaneous blow-up rates are established under different dominations of nonlinearities, and simply represented in a characteristic algebraic system introduced for the problem. In particular, it is observed that two of the multiple blow-up rates are absorption-related. This is substantially different from those for nonlinear parabolic problems with absorptions in all the previous literature, where the blow-up rates were known as absorption-independent. The results of the paper rely on the scaling method with a complete classification for the nonlinear parameters of the model. The first example of absorption-related blow-up rates was recently proposed by the authors for a coupled parabolic system with mixed type nonlinearities. The present paper shows that the newly observed phenomena of absorption-related blow-up rates should be due to the coupling mechanism, rather than the mixed type nonlinearities.