Open AccessSemilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up
Author(s) -
Jincheng Shi,
Yan Zhang,
Zihan Cai,
Yan Liu
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022015
Subject(s) - mathematics , type (biology) , derivative (finance) , nonlinear system , mathematical analysis , mathematical physics , physics , quantum mechanics , ecology , financial economics , economics , biology
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 ] .