Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term

Jincheng Shi; Jianye Xia; Wenjing Zhi; Jincheng Shi; Jianye Xia; Wenjing Zhi

doi:10.3934/math.2021634

AIMS Mathematics

2021, Volume 6, Issue 10: 10907-10919. doi: 10.3934/math.2021634

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Research article

Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term

1.
Department of Applied Mathematics, Guangzhou Huashang College, Guangzhou, China
2.
Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, China
3.
Department of Statistics, Beijing Normal University-Hong Kong Baptist University United International College, Zhuhai, China

Received: 10 June 2021 Accepted: 12 July 2021 Published: 28 July 2021
MSC : Primary: 35L71, 35B44; Secondary: 35B33

In this paper, we investigate blow-up conditions for the semilinear generalized Tricomi equation with a general nonlinear memory term in $ \mathbb{R}^n $ by using suitable functionals and employing iteration procedures. Particularly, a new combined effect from the relaxation function and the time-dependent coefficient is found.
- wave equation,
- semilinear hyperbolic equation,
- generalized Tricomi operator,
- blow-up,
- nonlinear memory term
Citation: Jincheng Shi, Jianye Xia, Wenjing Zhi. Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term[J]. AIMS Mathematics, 2021, 6(10): 10907-10919. doi: 10.3934/math.2021634

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Abstract

In this paper, we investigate blow-up conditions for the semilinear generalized Tricomi equation with a general nonlinear memory term in $ \mathbb{R}^n $ by using suitable functionals and employing iteration procedures. Particularly, a new combined effect from the relaxation function and the time-dependent coefficient is found.

References

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