Blow-up phenomena for a class of fourth order parabolic equation

A class of fourth order parabolic equation is studied in this paper. Some related blow-up results are obtained by applying the potential well theory, the concavity method and a series of differential-integral inequality techniques. More precisely, under some proper assumptions, the upper and lower b...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-01, Vol.505 (1), p.125445, Article 125445
Main Authors: Shao, Xiangkun, Tang, Guo-ji
Format: Article
Language:English
Subjects:
Blow up
Blow-up rate
Fourth-order parabolic equation
Lower bound
Upper bound
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Summary:A class of fourth order parabolic equation is studied in this paper. Some related blow-up results are obtained by applying the potential well theory, the concavity method and a series of differential-integral inequality techniques. More precisely, under some proper assumptions, the upper and lower bounds of the blow-up time and the growth rate for blow-up solutions are estimated. Moreover, a new blow-up condition independent of the depth of the potential well is found. These results complement the recent results obtained in Han (2018).
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125445