A note on blow-up in parabolic equations with local and localized sources
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Abstract:
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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Journal title
volume 43 issue 3
pages 923- 942
publication date 2017-06-01
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