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Indexed by:期刊论文

Date of Publication:2008-02-01

Journal:FRONTIERS OF MATHEMATICS IN CHINA

Included Journals:SCIE

Volume:3

Issue:1

Page Number:87-99

ISSN No.: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.