In this paper, we begin by establishing local well-posedness for the semilinear regular Euler-Poisson-Darboux-Tricomi equation. Subsequently, we derive a lifespan estimate with the Strauss index given by $p=p_{ S}(n+\frac{ \mu}{ m+1}, m)$ for any $\delta>0$, where $\delta$ is a parameter to describe the interplay between damping and mass. This is achieved through the construction of a new test function derived from the Gaussian hypergeometric function and a second-order ordinary differential inequality, as proven by Zhou \cite{ Zhou2014}. Additionally, we extend our analysis to prove a blow-up result with the index $p=\max\{ p_{ S}(n+\frac{ \mu}{ m+1}, m), p_{ F}((m+1)n+\frac{ \mu-1-\sqrt\delta}{ 2})\}$ by applying Kato$^{ \prime}$s Lemma ( i.e., Lemma \ref{ katolemma} ), specifically in the case of $\delta=1$.
Categories: math.AP
