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

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 $p>1+4/n$ ( $n\le 6$) or $p\ge 2-2/n$ ( $n\ge 7$), and blow-up of nontrivial weak solutions if $1<p\le 1+1/n$. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by ^[4].