A blow-up result for the semilinear Euler-Poisson-Darboux-Tricomi equation with critical power nonlinearity

2024/05/25 by N. Lai, Lai, Ning-An, Alessandro Palmieri +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2405.16145

openalex publication_date 2024/05/25 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a blow-up result for a generalized semilinear Euler-Poisson-Darboux equation with polynomially growing speed of propagation, when the power of the semilinear term is a shift of the Strauss' exponent for the classical semilinear wave equation. Our proof is based on a comparison argument of Kato-type for a second-order ODE with time-dependent coefficients, an integral representation formula by Yagdjian and the Radon transform. As byproduct of our method, we derive upper bound estimates for the lifespan which coincide with the sharp one for the classical semilinear wave equation in the critical case.

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