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

Source abstract

&lt;abstract&gt;&lt;p&gt;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 &lt;sup&gt;[&lt;xref ref-type="bibr" rid="b4"&gt;4&lt;/xref&gt;]&lt;/sup&gt;.&lt;/p&gt;&lt;/abstract&gt;