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 |uₜ|ᵖ. We demonstrate global existence of small data solutions if $ p > 1+4/n $ (n≤ 6) or p≥ 2-2/n (n≥ 7), and blow-up of nontrivial weak solutions if 1 < p≤ 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 ].