Liu, B., Li, F. (2017). A note on blow-up in parabolic equations with local and localized sources. Bulletin of the Iranian Mathematical Society, 43(3), 923-942.

B. Liu; F. Li. "A note on blow-up in parabolic equations with local and localized sources". Bulletin of the Iranian Mathematical Society, 43, 3, 2017, 923-942.

Liu, B., Li, F. (2017). 'A note on blow-up in parabolic equations with local and localized sources', Bulletin of the Iranian Mathematical Society, 43(3), pp. 923-942.

Liu, B., Li, F. A note on blow-up in parabolic equations with local and localized sources. Bulletin of the Iranian Mathematical Society, 2017; 43(3): 923-942.

A note on blow-up in parabolic equations with local and localized sources

^{}College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, P.R. China; Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA.

Receive Date: 04 October 2015,
Revise Date: 31 March 2016,
Accept Date: 14 April 2016

Abstract

This note deals with the systems of parabolic equations with local and localized sources involving $n$ components. We obtained the exponent regions, where $k\in \{1,2,\cdots,n\}$ components may blow up simultaneously while the other $(n-k)$ ones still remain bounded under suitable initial data. It is proved that different initial data can lead to different blow-up phenomena even in the same exponent regions, and moreover, different blow-up mechanism leads to different blow-up rates and blow-up sets.

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