Blow‐Up Result for a Weakly Coupled System of Two Euler–Poisson–Darboux–Tricomi Equations With Time Derivative Nonlinearity

ABSTRACT We study in this article the blowup of solutions to a coupled semilinear wave equations that are characterized by linear damping terms in the scale‐invariant regime , time‐derivative nonlinearities, mass, and Tricomi terms. The latter are specifically of great interest from both physical and mathematical points of view as they allow the speeds of propagation to be time‐dependent ones. However, we assume in this work that both waves are propagating with the same speeds. Employing this fact together with other hypotheses on the aforementioned parameters (mass and damping coefficients), we obtain a new blow‐up region for the system under consideration, and we show a lifespan estimate of the maximal existence time.