Nonexistence result for the generalized Tricomi equation with the scale-invariant damping, mass term and time derivative nonlinearity

This is the authors' abstract. We don't add key points for this paper.

In this article, we consider the damped wave equation in the scale-invariant case with time-dependent speed of propagation, mass term and time derivative nonlinearity. More precisely, we study the blow-up of the solutions to the following equation: [Formula: see text] that we associate with small initial data. Assuming some assumptions on the mass and damping coefficients, ν and [Formula: see text], respectively, we prove that blow-up region and the lifespan bound of the solution of [Formula: see text] remain the same as the ones obtained for the case without mass, i.e. [Formula: see text] with [Formula: see text] which constitutes itself a shift of the dimension N by [Formula: see text] compared to the problem without damping and mass. Finally, we think that the new bound for p is a serious candidate to the critical exponent which characterizes the threshold between the blow-up and the global existence regions.