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

Abstract

<abstract><p>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 <sup>[<xref ref-type="bibr" rid="b4">4</xref>]</sup>.</p></abstract>