具有内吸收和耦合局部化源的抛物组的渐近分析

Abstract

Abstract:

This paper deals with asymptotic analysis to a parabolic model with absorptions and coupled localized sources, for which it is shown that any blow-up occurs everywhere in the domain with one of three possible simultaneous blow-up rates under different dominations of nonlinearities. All the three blow-up rates are simply represented
in a characteristic algebraic system introduced for the problem. In particular, uniform blow-up profiles are established for the case of weak absorptions. While for the two cases of unbalanced absorptions, we establish uniform blow-up rates (instead of blow-up profiles) which are absorption-related. This is substantially different from scalar parabolic problems with absorptions in current literatures, where all the blow-up rates are known as
absorption-independent. The results of the paper mainly rely on the scaling method with a complete classification for the nonlinear parameters in the model.

Key words: Localized sources, Absorption, Blow-up profile, Blow-up rates, Characteristic algebraic system

CLC Number:

35B40

KONG Ling-Hua, ZHAO Li-Zhong, ZHENG Shi-Ning. Asymptotic Analysis to Parabolic Equations with Absorptions and Coupled Localized Sources[J].Acta mathematica scientia,Series A, 2010, 30(1): 267-277.

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Asymptotic Analysis to Parabolic Equations with Absorptions and Coupled Localized Sources

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