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In this note, we prove blow-up results for semilinear wave models withdamping and mass in the scale-invariant case and with nonlinear terms ofderivative type. We consider the single equation and the weakly coupled system.In the first case we get a blow-up result for exponents below a certain shiftof the Glassey exponent. For the weakly coupled system we find as criticalcurve a shift of the corresponding curve for the weakly coupled system ofsemilinear wave equations with the same kind of nonlinearities. Our approachfollows the one for the respective classical wave equation by Zhou Yi. Inparticular, an explicit integral representation formula for a solution of thecorresponding linear scale-invariant wave equation, which is derived by usingYagdjian's integral transform approach, is employed in the blow-up argument.While in the case of the single equation we may use a comparison argument, forthe weakly coupled system an iteration argument is applied.

A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type