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

Document Type : Research Paper


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.


‎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.


Main Subjects

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