Upper and lower bounds for the blow-up time of a fourth-order parabolic equation with exponential nonlinearity

Shuting Chang; Yaojun Ye; Shuting Chang; Yaojun Ye

doi:10.3934/era.2024289

Electronic Research Archive

2024, Volume 32, Issue 11: 6225-6234. doi: 10.3934/era.2024289

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Research article

Upper and lower bounds for the blow-up time of a fourth-order parabolic equation with exponential nonlinearity

Shuting Chang ,
Yaojun Ye ^,

Department of Mathematics and Statistics, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received: 12 September 2024 Revised: 24 October 2024 Accepted: 13 November 2024 Published: 18 November 2024

This paper investigated the blow-up properties of solutions to the initial value problem for a fourth-order nonlinear parabolic equation with an exponential source term. By using an improved concavity method, we obtained upper and lower bound estimates for the blow-up time of the solution.
- fourth-order parabolic equation,
- exponential source term,
- Cauchy problem,
- blow-up,
- upper and lower bounds for the blow-up time
Citation: Shuting Chang, Yaojun Ye. Upper and lower bounds for the blow-up time of a fourth-order parabolic equation with exponential nonlinearity[J]. Electronic Research Archive, 2024, 32(11): 6225-6234. doi: 10.3934/era.2024289

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Abstract

This paper investigated the blow-up properties of solutions to the initial value problem for a fourth-order nonlinear parabolic equation with an exponential source term. By using an improved concavity method, we obtained upper and lower bound estimates for the blow-up time of the solution.

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