Existence of solutions of semilinear wave equations with time-dependent propagation speed and time derivative nonlinearity

2025/05/17 by Kimitoshi Tsutaya, Tsutaya, Kimitoshi, Yuta Wakasugi +1 · 1 citation
Mathematics · Physics and Astronomy · #35L05 #35L70 #35Q85 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2505.11798

openalex publication_date 2025/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider wave equations with time derivative nonlinearity and time-dependent propagation speed which are generalized versions of the wave equations in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, the de Sitter spacetime and the anti-de Sitter space time. We show lower bounds of the lifespan of solutions as well as the global existence by providing an integrability condition on the propagation speed function, which is applicable to the nonlinear wave equation in the expanding FLRW spacetime including the de Sitter spacetime. We also prove that blow-up in a finite time occurs for the generalized form of the equation in contracting universes such as the anti-de Sitter spacetime, as well as upper bounds of the lifespan of blow-up solutions.

Citations

• Fractional derivatives of composite functions and the Cauchy problem for the nonlinear half wave equation

Cited by

• Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes

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