Blow-Up Phenomenon of Solution to the Semilinear Viscous Moore-Gibson-Thompson Equation With Memory Terms

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 Nγ,\,q(u), Nγ,\,p(uₜ), Nγ,\,p,\,q(u,\,uₜ) 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 γ→1⁻. Up to author's best knowledge, the results in Theorems 1.1-1.3 are new.