BLOW-UP PHENOMENON OF SOLUTION TO THE SEMILINEAR VISCOUS MOORE-GIBSON-THOMPSON EQUATION WITH MEMORY TERMS

Abstract

This article is devoted to investigating the initial boundary value problem of semilinear viscous Moore-Gibson-Thompson equation with general initial values and nonlinear memory terms $N_{\gamma,\,q}(u)$, $N_{\gamma,\,p}(u_{t})$, $N_{\gamma,\,p,\,q}(u,\,u_{t})$ on exterior domain, respectively. Blow-up dynamic of solution is deduced by taking advantage of the test function method related to an appropriate harmonic function. It is worth observing that the semilinear viscous Moore-Gibson-Thompson equation with memory terms can be considered as an approximation of viscous Moore-Gibson-Thompson equation with nonlinear terms when $\gamma\rightarrow1^{-}$. Up to author's best knowledge, the results in Theorems 1.1-1.3 are new.