Critical curve for weakly coupled system of semilinear Euler-Poisson-Darboux-Tricomi equations

2025/11/11 by Li, Yuequn, Guo, Fei
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.08084

Abstract

This paper investigates a weakly coupled system of semilinear Euler-Poisson-Darboux-Tricomi equations (EPDTS) with power-type nonlinear terms. More precisely, in the case where the damping terms dominate over the mass terms, the critical curve in the p-q plane that delineates the threshold between global existence and blow-up for the EPDTS is given by Γ_m(n,p,q,β₁,β₂)=0, where Γ_m is defined by (\refgammam). Through the construction of new test functions, the blow-up problem is addressed when Γ_m(n,p,q,β₁,β₂)≥0. Based on the (L¹∩ L²)-L² estimates of the solution to the corresponding linear equation established in our previous work \citeLiGuo2025, we derive the global existence of solutions with small initial data when Γ_m(n,p,q,β₁,β₂)<0, provided that the damping terms prevail over the mass terms.

Citations

• On semilinear Tricomi equations with critical exponents or in two space dimensions
• On the global solution problem for semilinear generalized Tricomi equations, I
• Life-Span of Solutions to Critical Semilinear Wave Equations
• Finite time blow up for critical wave equations in high dimensions

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