A blow – up result for the semilinear moore – gibson – thompson equation with nonlinearity of derivative type in the conservative case

In this paper, we study the blow-up of solutions to the semilinear Moore – Gibson – Thompson (MGT) equation with nonlinearity of derivative type |ut|p in the conservative case. We apply an iteration method in order to study both the subcritical case and the critical case. Hence, we obtain a blow-up result for the semilinear MGT equation (under suitable assumptions for initial data) when the exponent p for the nonlinear term satisfies 1 < p ≤ (n+1)/(n−1) for n ≥ 2 and p > 1 for n = 1. In particular, we find the same blow-up range for p as in the corresponding semilinear wave equation with nonlinearity of derivative type.