Non-simultaneous blow-up of n components for nonlinear parabolic systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:356

Article

Liu, Bingchen¹  Li, Fengjie¹ 

[1] China Univ Petr, Coll Math & Computat Sci, Dongying 257061, Shandong, Peoples R China

关键词: Non-simultaneous blow-up;    Simultaneous blow-up;    Blow-up rate;    Blow-up set;   

DOI  :  10.1016/j.jmaa.2009.03.018

来源: Elsevier

【 摘 要 】

This paper deals with non-sirnultaneous and simultaneous blow-up for radially symmetric Solution (u(1), u(2),..., u(n)) to heat equations coupled via nonlinear boundary partial derivative uj/partial derivative eta = u(i)(pi) u(i+1)(q1+1) (i = 1, 2,..., n). It is proved that there exist suitable initial data Such that Ui (i is an element of {1, 2..., n}) blows up alone if and only if q(i) + 1 < p(i). All of the classifications oil the existence of only two components blowing Lip simultaneously are obtained. We find that different positions (different values of k, i, n) of u(i-k) and u(i) leads to quite different blow-up rates. It is interesting that different initial data lead to different blow-up phenomena even with the same requirements on exponent parameters. We also propose that u(i-k). u(i-k+1).....u(i) (i is an element of {1, 2,...,n), k is an element of {0, 1, 2,..., n - 1}) blow LIP simultaneously while the other ones remain bounded in different exponent regions. Moreover, the blow-up rates and blow-up sets are obtained. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free