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

Fujita versus Strauss - a never ending story