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 blowup phenomenon for the solution in the whole space is based on the test function method (psi(x, t) = phi(R)(x)D-t vertical bar 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 -> 1(-). To the best of our knowledge, the results in Theorems 1.1-1.3 are new.