Small data blow-up for the weakly coupled system of the generalized Tricomi equations with multiple propagation speeds

Ikeda, Masahiro; Lin, Jiayun; Tu, Ziheng

doi:10.1007/s00028-021-00703-4

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2021

2024

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Cited by 7 publications

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“…For other types of nonlinearities in systems similar to (1.11), we refer the reader to [17] for the case of combined nonlinearities and [5] for power nonlinearities.…”

Section: Introductionmentioning

confidence: 99%

Blow-up result for a weakly coupled system of wave equations with a scale-invariant damping, mass term and time derivative nonlinearity

Hassen,

Hamouda,

Hamza

2024

Preprint

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We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass and Tricomi terms. The latter are specifically of great interest from both physical and mathematical points of view since they allow the speeds of propagation to be time-dependent ones. However, we assume in this work that both waves are propagating with the same speeds. Employing this fact together with other hypotheses on the aforementioned parameters (mass and damping coefficients), we obtain a new blow-up region for the system under consideration, and we show a lifespan estimate of the maximal existence time.

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“…For other types of nonlinearities in systems similar to (1.11), we refer the reader to [17] for the case of combined nonlinearities and [5] for power nonlinearities.…”

Section: Introductionmentioning

confidence: 99%