A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

<p style='text-indent:20px;'>In this paper, we study the blow – up of solutions to semilinear Moore Gibson Thompson (MGT) equation with nonlinearity derivative type <inline-formula><tex-math id="M1">\begin{document}$ |u_t|^p $\end{document}</tex-math></inline-formula> in conservative case. We apply an iteration method order both subcritical case and critical Hence, obtain a result for MGT (under suitable assumptions initial data) when exponent id="M2">\begin{document}$ p nonlinear term satisfies id="M3">\begin{document}$ 1<p\leqslant (n+1)/(n-1) id="M4">\begin{document}$ n\geqslant2 id="M5">\begin{document}$ p>1 id="M6">\begin{document}$ n = 1 $\end{document}</tex-math></inline-formula>. In particular, find same range id="M7">\begin{document}$ as corresponding wave type.</p>