Finite time blow-up for a semilinear generalized Tricomi system with mixed nonlinearity

Fan, Mengting; Geng, Jianhua; Lai, N.; Lin, Jiayun

doi:10.1016/j.nonrwa.2022.103613

Cited by 4 publications

(1 citation statement)

References 23 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%

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

View full text Add to dashboard Cite

show abstract

Blow-up of solutions to the wave equations with memory terms in Schwarzschild spacetime

Ming,

Du,

Xie

2024

Journal of Mathematical Analysis and Applications

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Blow-up of solution to semilinear wave equations with strong damping and scattering damping

Ming

et al. 2022

Bound Value Probl

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This paper is devoted to investigating the initial boundary value problem for a semilinear wave equation with strong damping and scattering damping on an exterior domain. By introducing suitable multipliers and applying the test-function technique together with an iteration method, we derive the blow-up dynamics and an upper-bound lifespan estimate of the solution to the problem with power-type nonlinearity $|u|^{p}$ | u | p , derivative-type nonlinearity $|u_{t}|^{p}$ | u t | p , and combined type nonlinearities $|u_{t}|^{p}+|u|^{q}$ | u t | p + | u | q in the scattering case, respectively. The novelty of the present paper is that we establish the upper-bound lifespan estimate of the solution to the problem with strong damping and scattering damping, which are associated with the well-known Strauss exponent and Glassey exponent.

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Finite time blow-up for a semilinear generalized Tricomi system with mixed nonlinearity

Cited by 4 publications

References 23 publications

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

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

Blow-up of solutions to the wave equations with memory terms in Schwarzschild spacetime

Blow-up of solution to semilinear wave equations with strong damping and scattering damping

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