Blow-up dynamic of solution to the semilinear Moore-Gibson-Thompson equation with memory terms

This article is mainly concerned with the formation of singularity for a solution to the Cauchy problem of the semilinear Moore-Gibson-Thompson equation with general initial values and different types of nonlinear memory terms $N_{\gamma ,q}(u)$, $N_{\gamma ,p}(u_t)$, $N_{\gamma ,p,q}(u,u_t)$. The proof of the blow-up phenomenon for the solution in the whole space is based on the test function method ( $\psi (x,t)={\phi }_R(x)D_{t|T}^{\alpha }(w(t))$). It is worth pointing out that the Moore-Gibson-Thompson equation with memory terms can be regarded as an approximation of the nonlinear Moore-Gibson-Thompson equation when $\gamma \to 1^{-}$. To the best of our knowledge, the results in Theorems 1.1–1.3 are new.