Blow-Up Profile of Solutions in Parabolic Equations with Nonlocal Dirichlet Conditions

This paper deals with parabolic equations with nonlocal Dirichlet boundary conditions. Critical exponent and simultaneous blow-up criteria are studied for blow-up solutions. Moreover, we determine uniform blow-up profiles and blow-up set to all kinds of simultaneous blow-up solutions. It is interest...

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Bibliographic Details
Published in:Bulletin of the Iranian Mathematical Society 2020-10, Vol.46 (5), p.1437-1453
Main Authors: Liu, Bingchen, Zhang, Changcheng, Wei, Yu
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Original Paper
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Summary:This paper deals with parabolic equations with nonlocal Dirichlet boundary conditions. Critical exponent and simultaneous blow-up criteria are studied for blow-up solutions. Moreover, we determine uniform blow-up profiles and blow-up set to all kinds of simultaneous blow-up solutions. It is interesting that large weighted functions could provide sufficient help to the occurring of blow-up of solutions without conditions on initial data.
ISSN:1017-060X
1735-8515
DOI:10.1007/s41980-019-00334-z