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研究论文
一类非线性抛物系统不同时爆破后的雪崩现象
Avalanche After Non-simultaneous Blow-up in Nonlinear Parabolic Systems

刘丙辰,李锋杰
LIU Bingchen*,LI Fengjie

中国石油大学(华东)数学与计算科学学院,青岛,山东, 266555
College of Mathematics and Computational Science, China University of Petroleum(Huadong), Qingdao, Shandong, 266555, P. R. China

收稿日期: 2011-04-11
出版日期: 2013-08-25
DOI: 10.11845/sxjz.20130417b

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摘要 本文研究一类具有非线性边界流的热方程组解的完全爆破问题. 首先, 完善了已有研究结果中爆破解的完全分类, 并得到爆破集由单个点组成, 然后证明了该方程组问题的爆破总是完全的. 有趣的是, 即使出现不同时爆破现象, 雪崩总会发生, 也即解的爆破奇性在有限爆破时刻后会瞬间传播到整个空间区域.
关键词 不同时爆破爆破集完全爆破雪崩    
Abstract:This paper cares about whether blow-up is complete or not for some heat equations with coupled nonlinear flux. First, we finish the classifications on blow-up solutions in the previous paper, and obtain that blow-up set is made up of only a single point. Then we prove that blow-up is always complete. It is interesting that, even if non-simultaneous blow-up happens, avalanche phenomena occur after the finite blow-up time, which means that blow-up singularity propagates instantaneously to the whole spatial domain after that time.
Key wordsblow-up set    complete blow-up    avalanche
基金资助:This paper is partially supported by NSFC (No. 11201483), Shandong Provincial Natural Science Foundation (No. ZR2010AQ011), and the Fundamental Research Funds for the Central Universities (No. 11CX04058A, No. 12CX04081A).
通讯作者: *bclfjl@yahoo.com.cn   
[1] 刘丙辰,李锋杰,郑斯宁. 一类反映扩散系统的不同时爆破临界指标 (英)[J]. 数学进展, 2011, 40(5): 531-536.
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