BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS

Xiongmei Fan; Sen Ming

doi:10.11948/20260114

2027 Volume 17 Issue 2

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Article navigation > Journal of Applied Analysis & Computation > 2027 > 17(2): 1232-1252

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Xiongmei Fan, Sen Ming. BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1232-1252. doi: 10.11948/20260114

Citation:

Xiongmei Fan, Sen Ming. BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS[J]. Journal of Applied Analysis & Computation, 2027, 17(2): 1232-1252. doi: 10.11948/20260114

BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS

Xiongmei Fan^1,,
Sen Ming^2, ,

1.
Department of Mathematics, Jinzhong University, Jinzhong 030619, China
2.
Department of Mathematics, North University of China, Taiyuan 030051, China

Author Bio: Email: xiongmeifan1997@163.com(X. Fan)
Corresponding author: Email: senming1987@163.com(S. Ming)
Fund Project: The project is supported by Fundamental Research Program of Shanxi Province (No. 202403021212254, No. 202303021212267), Education Science Research Project of Shanxi Provincial (No. SZH-230066), Graduate Course Ideological and Political Demonstration Project of Shanxi Provincial (No. 2025SZ11), Jinzhong University Research Funds for Doctor (No. 23E00628), The Second Batch of Reward Funds for Outstanding Doctors Coming to Shanxi in 2025 (No. 20625D243030)

Abstract

Abstract

This article is devoted to investigating the initial boundary value problem of semilinear viscous Moore-Gibson-Thompson equation with general initial values and nonlinear memory terms $N_{\gamma,\,q}(u)$, $N_{\gamma,\,p}(u_{t})$, $N_{\gamma,\,p,\,q}(u,\,u_{t})$ on exterior domain, respectively. Blow-up dynamic of solution is deduced by taking advantage of the test function method related to an appropriate harmonic function. It is worth observing that the semilinear viscous Moore-Gibson-Thompson equation with memory terms can be considered as an approximation of viscous Moore-Gibson-Thompson equation with nonlinear terms when $\gamma\rightarrow1^{-}$. Up to author's best knowledge, the results in Theorems 1.1-1.3 are new.
- Viscous Moore-Gibson-Thompson equation /
- general initial values /
- nonlinear memory terms /
- exterior domain /
- blow-up
MSC: 35L70, 58J45

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References

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