Global existence for the semilinear regular Euler-Poisson-Darboux-Tricomi equation, II

Abstract

In our previous work [25], we established the global existence of solutions to the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity \(|u|^p\) in the case where the damping term dominates the mass term. In contrast, this paper studies the reverse case, namely, the existence of global solutions to the equation when the mass term dominates the damping term. We prove that small-data solutions exist globally if \[ p>\max\{p_0((m+1)n,μ), \widetilde{p}_1(n,m,μ)\} \] for \(δ\doteq(μ-1)^2-4ν^2\leq0\), where \(δ\) measures the relative dominance between the damping and mass terms, \(p_0(n,μ)\) is the \textit{Strauss-related} exponent defined by (1.12), and \(\widetilde{p}_1(n,m,μ)\) is defined by (2.5).