Blow-up upper and lower bounds for solutions of a class of higher order nonlinear pseudo-parabolic equations

Qianqian Zhu; Yaojun Ye; Shuting Chang; Qianqian Zhu; Yaojun Ye; Shuting Chang

doi:10.3934/era.2024046

Electronic Research Archive

2024, Volume 32, Issue 2: 945-961. doi: 10.3934/era.2024046

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Research article

Blow-up upper and lower bounds for solutions of a class of higher order nonlinear pseudo-parabolic equations

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

Received: 28 August 2023 Revised: 28 November 2023 Accepted: 12 December 2023 Published: 16 January 2024

In this paper, we study the initial boundary value problem for a class of higher-order nonlinear pseudo-parabolic equations with a memory term. First, the blow-up results of the solution when the initial energy is negative or positive are obtained by using concavity analysis, and an upper bound on the blow-up time $ T^* $ is given. Second, a lower bound on the blow-up time $ T^* $ is obtained by applying differential inequalities when the solutions blow up.
- higher order pseudo-parabolic equation,
- memory term,
- blow-up,
- upper bound,
- lower bound
Citation: Qianqian Zhu, Yaojun Ye, Shuting Chang. Blow-up upper and lower bounds for solutions of a class of higher order nonlinear pseudo-parabolic equations[J]. Electronic Research Archive, 2024, 32(2): 945-961. doi: 10.3934/era.2024046

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Abstract

In this paper, we study the initial boundary value problem for a class of higher-order nonlinear pseudo-parabolic equations with a memory term. First, the blow-up results of the solution when the initial energy is negative or positive are obtained by using concavity analysis, and an upper bound on the blow-up time $ T^* $ is given. Second, a lower bound on the blow-up time $ T^* $ is obtained by applying differential inequalities when the solutions blow up.

References

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