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 blow-up of solutions to a coupled
semilinear wave equations which 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 since
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.