Blow-up phenomena for a class of fourth order parabolic equation |
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Authors: | Xiangkun Shao Guo-ji Tang |
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Affiliation: | 1. School of Mathematics, Sichuan University, Sichuan, 610064, PR China;2. School of Mathematics and Physics, Guangxi University for Nationalities, Guangxi, 530006, PR China;3. Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi, 530006, PR China |
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Abstract: | 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). |
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Keywords: | Fourth-order parabolic equation Blow up Upper bound Lower bound Blow-up rate |
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