Abstract
This paper is concerned with the blow-up property of solutions to an initial boundary value problem for a fourth-order parabolic equation with a general nonlinearity. It is shown, under certain conditions on the initial data, that the solutions to this problem blow up in finite time, using differential inequalities. Moreover, upper and lower bounds for the blow-up time are derived when blow-up occurs. This extends and generalizes results obtained by Philippin (Proc AMS. 2015;143(6):2507–13) and by Han (Nonlinear Anal RWA. 2018;43:451–66).
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Acknowledgments
The author wishes to express his gratitude to the anonymous referee for giving a number of valuable comments and helpful suggestions, which improve the presentation of the original manuscript significantly. He would also like to express his sincere gratitude to Professor Wenjie Gao for his enthusiastic guidance and constant encouragement and to Professor Bin Guo for some valuable discussion when proving Theorem 4.1.
Funding
This work is supported by NSFC (11401252) and by The Education Department of Jilin Province (JJKH20190018KJ).
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Han, Y. Blow-Up Phenomena for a Fourth-Order Parabolic Equation with a General Nonlinearity. J Dyn Control Syst 27, 261–270 (2021). https://doi.org/10.1007/s10883-020-09495-1
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DOI: https://doi.org/10.1007/s10883-020-09495-1