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

نویسندگان

  • B. Liu 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.
  • F. Li 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.
چکیده مقاله:

‎This note deals with the systems of parabolic equations with local and localized sources involving $n$ components‎. ‎We obtained the exponent regions‎, ‎where $kin {1,2,cdots,n}$ 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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عنوان ژورنال

دوره 43  شماره 3

صفحات  923- 942

تاریخ انتشار 2017-06-01

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