Nonexistence of global solutions for the semilinear Moore - Gibson - Thompson equation in the conservative case

In this work, the Cauchy problem for the semilinear Moore-Gibson -Thompson (MGT) equation with power nonlinearity jujp on the right - hand side is studied. Applying L2-L2estimates and a fixed point theorem, we obtain local (in time) existence of solutions to the semilinear MGT equation. Then, the blow - up of local in time solutions is proved by using an iteration method, under certain sign assumption for initial data, and providing that the exponent of the power of the nonlinearity fulfills 1 < p ≤ pStr(n) for n > 2 and p > 1 for n = 1. Here the Strauss exponent pStr(n) is the critical exponent for the semilinear wave equation with power nonlinearity. In particular, in the limit case p = pStr(n) a different approach with a weighted space average of a local in time solution is considered.