@article{Ming2023, 
author = {Sen Ming and Xiongmei Fan and Cui Ren and Yeqin Su},
title = {Blow-up dynamic of solution to the semilinear Moore-Gibson-Thompson equation with memory terms},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {4630-4644},
keywords = {blow-up, Moore-Gibson-Thompson equation, general initial values, nonlinear memory terms, test function method},
url = {https://www.sciopen.com/article/10.3934/math.2023228},
doi = {10.3934/math.2023228},
abstract = {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          γ      ,            q        (  u  ),        N          γ      ,            p        (      u          t        ),        N          γ      ,            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 (   ψ  (  x  ,  t  )  =      φ          R        (  x  )      D          t              |            T              α        (  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    γ  →      1          −      . To the best of our knowledge, the results in Theorems 1.1–1.3 are new.}
}