Blow-up and lifespan estimate for generalized Tricomi equations related to Glassey conjecture

Lai, N.; Schiavone, Nico Michele

doi:10.1007/s00209-022-03017-4

Cited by 14 publications

(5 citation statements)

References 38 publications

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“…• we expect global (in time) existence of solutions with the range γ > 1 so that C Gla = 0, which stands for the supercritical nonlinearity case. [12], the wave model with scale-invariant damping (and mass) [12,17], the damped wave model in the Einstein-de Sitter spacetime [6], and the generalized Tricomi equations [13].…”

Section: Iteration Procedures and Blow-up Whenmentioning

confidence: 99%

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A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

Chen¹,

Palmieri²

2021

EECT

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In this paper, we study the blow-up of solutions to the semilinear Moore-Gibson-Thompson (MGT) equation with nonlinearity of derivative type |ut| p in the conservative case. We apply an iteration method in order to study both the subcritical case and the critical case. Hence, we obtain a blow-up result for the semilinear MGT equation (under suitable assumptions for initial data) when the exponent p for the nonlinear term satisfies 1 < p (n + 1)/(n − 1) for n 2 and p > 1 for n = 1. In particular, we find the same blow-up range for p as in the corresponding semilinear wave equation with nonlinearity of derivative type.

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Section: Iteration Procedures and Blow-up Whenmentioning

confidence: 99%

“…and its related models (e.g. on asymptotically flat manifolds [25], on asymptotically Euclidean manifolds [14], in Friedmann-Lemaître-Robertson-Walker spacetime [23], with time-dependent propagation speed [15,13]) have been widely investigated by the PDE community. Particularly, the critical exponent, i.e.…”

Section: Introductionmentioning

confidence: 99%

A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

Chen¹,

Palmieri²

2021

EECT

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show abstract

“…Here, 𝛾, 𝛽 ∈ (0, +∞) and p, q ∈ (1, +∞). As in earlier studies [20][21][22], by the application of L 2 -estimates developed in this paper, it is very interesting to explore the relation between critical index which divides the supercritical case and subcritical case and the oscillating types of the time-dependent coefficients. Continuing efforts will be devoted to the analysis of these open problems, including the main challenges such as global existence of small initial data solution and lifespan of the finite-time blow-up solution.…”

Section: Discussionmentioning

confidence: 76%

On the quadratic wave equation with randomized oscillating coefficients

2023

Math Methods in App Sciences

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In this paper, we consider the asymptotic behavior of the solutions of the quadratic wave equations with perturbed oscillating coefficients which are very important mathematical models in describing the oscillation of particles imposed with time‐dependent electromagnetic fields. By the application of microlocal analysis and stochastic analysis, this paper makes a delicate classification of various types of time‐dependent oscillating coefficients on the principal quantum harmonic oscillator part and explores the corresponding regularity behavior and L2$$ {L}&amp;amp;amp;amp;#x0005E;2 $$‐estimates of the solution of the equation. It is interesting to find out that weak or mild oscillations will not cause any energy growth, while regular and strong oscillations will lead to polynomial or exponential growth of the energy. This is meaningful to help us explore the energy conversion mechanism in the electromagnetic field. Furthermore, in order to demonstrate the optimality of the L2$$ {L}&amp;amp;amp;amp;#x0005E;2 $$‐estimates, typical counterexamples with periodic coefficients will be constructed to show the lower bound of growth rate by the application of harmonic analysis and instability arguments. Compared with formal literatures focusing on the constant coefficients, current results in this paper reveal the essential relation between oscillation types and energy growth.

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“…For m > 0 and µ = ν = 0, blow-up results and lifespan estimate of the solution of the single equation corresponding to (1.1) are proven in [21], see also [22]. This yields a new region characterized by a plausible candidate for the critical exponent, namely (1.10) p ≤ p T (N, m)…”

Section: Introductionmentioning

confidence: 87%

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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Blow-up and lifespan estimate for generalized Tricomi equations related to Glassey conjecture

Cited by 14 publications

References 38 publications

A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

A blow – up result for the semilinear Moore – Gibson – Thompson equation with nonlinearity of derivative type in the conservative case

On the quadratic wave equation with randomized oscillating coefficients

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

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