Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up

Jincheng Shi; Yan Zhang; Zihan Cai; Yan Liu; Jincheng Shi; Yan Zhang; Zihan Cai; Yan Liu

doi:10.3934/math.2022015

AIMS Mathematics

2022, Volume 7, Issue 1: 247-257. doi: 10.3934/math.2022015

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Research article

Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up

1.
College of Data Sciences, Guangzhou Huashang College, Huashang Road, Guangzhou 511300, China
2.
Department of Applied Mathematics, Guangdong Teachers College of Foreign Language and Arts, Longdong East Road, , 510521, Guangzhou, China
3.
Department of Applied Mathematics, Guangdong University of Finance, Yingfu Road, 510521, Guangzhou, China

Received: 29 August 2021 Accepted: 30 September 2021 Published: 11 October 2021
MSC : 35A01, 35B40, 35B44, 35G25

In this paper, we study global existence and blow-up of solutions to the viscous Moore-Gibson-Thompson (MGT) equation with the nonlinearity of derivative-type $ |u_t|^p $. We demonstrate global existence of small data solutions if $ p > 1+4/n $ ($ n\leq 6 $) or $ p\geq 2-2/n $ ($ n\geq 7 $), and blow-up of nontrivial weak solutions if $ 1 < p\leq 1+1/n $. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by ^[4].
- Moore-Gibson-Thompson equation,
- derivative-type nonlinearity,
- global existence of small data solution,
- decay estimate,
- blow-up
Citation: Jincheng Shi, Yan Zhang, Zihan Cai, Yan Liu. Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up[J]. AIMS Mathematics, 2022, 7(1): 247-257. doi: 10.3934/math.2022015

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Abstract

In this paper, we study global existence and blow-up of solutions to the viscous Moore-Gibson-Thompson (MGT) equation with the nonlinearity of derivative-type $ |u_t|^p $. We demonstrate global existence of small data solutions if $ p > 1+4/n $ ($ n\leq 6 $) or $ p\geq 2-2/n $ ($ n\geq 7 $), and blow-up of nontrivial weak solutions if $ 1 < p\leq 1+1/n $. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by ^[4].

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