具有内吸收和耦合局部化源的抛物组的渐近分析

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 267-277.

具有内吸收和耦合局部化源的抛物组的渐近分析

孔令花, 赵立中, 郑斯宁

大连水产学院理学院大连 116023

收稿日期:2008-05-08 修回日期:2009-07-16 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
国家自然科学基金(10771024)资助

Asymptotic Analysis to Parabolic Equations with Absorptions and Coupled Localized Sources

KONG Ling-Hua, ZHAO Li-Zhong, ZHENG Shi-Ning

School of Science, Dalian |Fisheries University, Dalian 116023

Received:2008-05-08 Revised:2009-07-16 Online:2010-01-01 Published:2010-01-01
Supported by:
国家自然科学基金(10771024)资助

摘要/Abstract

摘要：

该文是关于一类具有内吸收和耦合局部化源的抛物组解的渐近分析的研究. 作者证明了解在区域内处处blow-up的结论, 得到不同非线性指标占优情形下三种可能的blow-up速率, 并借助于所引入的特征代数方程组给出这三种速率的简洁表示. 特别地, 作者对弱吸收情形, 给出解的一致blow-up profile; 对于两种非平衡吸收情形, 得到与吸收项指标有关的blow-up速率, 这与单个方程情形(其速率均与吸收项指标无关)的已有结果截然不同. 以上结果的证明主要依据scaling方法,以及对于模型非线性指标的完全分类.

关键词: 局部化源, 内吸收, Blow-up Profile, Blow-up速率, 特征代数方程组

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

中图分类号:

35B40

孔令花, 赵立中, 郑斯宁. 具有内吸收和耦合局部化源的抛物组的渐近分析[J]. 数学物理学报, 2010, 30(1): 267-277.

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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