Non-simultaneous blow-up of n components for nonlinear parabolic systems |
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Authors: | Bingchen Liu Fengjie Li |
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Institution: | College of Mathematics and Computational Science, China University of Petroleum, Dongying 257061, Shandong Province, PR China |
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Abstract: | This paper deals with non-simultaneous and simultaneous blow-up for radially symmetric solution (u1,u2,…,un) to heat equations coupled via nonlinear boundary (i=1,2,…,n). It is proved that there exist suitable initial data such that ui(i∈{1,2,…,n}) blows up alone if and only if qi+1<pi. All of the classifications on the existence of only two components blowing up simultaneously are obtained. We find that different positions (different values of k, i, n) of ui−k and ui 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 ui−k,ui−k+1,…,ui blow up simultaneously while the other ones remain bounded in different exponent regions. Moreover, the blow-up rates and blow-up sets are obtained. |
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Keywords: | Non-simultaneous blow-up Simultaneous blow-up Blow-up rate Blow-up set |
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