2025/02/04 by Li, Yuequn, Guo, Fei
#35B44 #35G25 #Analysis of PDEs (math.AP) #FOS: Mathematics #I.7.1
paper · doi:10.48550/arxiv.2502.02084
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=pS(n+\fracμm+1, m) for any δ>0, where δ 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 \citeZhou2014. Additionally, we extend our analysis to prove a blow-up result with the index p=max\pS(n+\fracμm+1, m), pF((m+1)n+(μ-1-√δ)/(2))\ by applying Kato′s Lemma ( i.e., Lemma \refkatolemma ), specifically in the case of δ=1.