Blow-up dynamic of solution to the semilinear Moore-Gibson-Thompson equation with memory terms

AIMS Mathematics

article

Sen Ming¹  Xiongmei Fan²  Cui Ren¹  Yeqin Su³ 

[1] Department of Mathematics, North University of China;Data Science And Technology, North University of China;Department of Securities and Futures, Southwestern University of Finance and Economics

关键词: Moore-Gibson-Thompson equation;    general initial values;    nonlinear memory terms;    blow-up;    test function method;   

DOI  :  10.3934/math.2023228

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

This article is mainly concerned with the formation of singularity for a solution to the Cauchy problem of the semilinear Moore-Gibson-Thompson equation with general initial values and different types of nonlinear memory terms $ N_{\gamma, \, q}(u) $, $ N_{\gamma, \, p}(u_{t}) $, $ N_{\gamma, \, p, \, q}(u, \, u_{t}) $. The proof of the blow-up phenomenon for the solution in the whole space is based on the test function method ($ \psi(x, t) = \varphi_{R}(x)D_{t|T}^{\alpha}(w(t)) $). It is worth pointing out that the Moore-Gibson-Thompson equation with memory terms can be regarded as an approximation of the nonlinear Moore-Gibson-Thompson equation when $ \gamma\rightarrow 1^{-} $. To the best of our knowledge, the results in Theorems 1.1–1.3 are new.

【 授权许可】

CC BY