  In this paper, we obtain a blow-up result for solutions to a semi-linear wave
equation with scale-invariant dissipation and mass and power non-linearity, in
the case in which the model has a "wave like" behavior.
  In order to achieve this goal, we perform a change of variables that
transforms our starting equation in a strictly hyperbolic semi-linear wave
equation with time-dependent speed of propagation.
  Then, we apply Kato's lemma to find a blow-up result for solutions to the
transformed equation under some support and sign assumptions on the initial
data. A special emphasis is placed on the limit case, that is, when the
exponent p is exactly equal to the upper bound of the range of admissible
values of p for which this blow-up result is valid. In this critical case an
explicit integral representation formula for solutions of the corresponding
linear Cauchy problem in 1d is derived.
  Finally, carrying out the inverse change of variables we get a non-existence
result for global (in time) solutions to the original model.
