Moore–Gibson–Thompson equation with memory in a history framework: a semigroup approach

Alves, Michele O.; Caixeta, A. H.; Silva, Marcio A. Jorge; Rodrigues, José Henrique

doi:10.1007/s00033-018-0999-5

Cited by 36 publications

(49 citation statements)

References 12 publications

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“…Over the last years, the Moore -Gibson -Thompson (MGT) equation (cf. [30,45]), a linearization of a model for the wave propagation in viscous thermally relaxing fluids, has been studied by several authors (see, for example, [13,20,19,28,18,27,7,11,26,12,25,37,3,10,38,5,6,4,8]).…”

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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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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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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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“…The same model with added memory, where the latter accounts for molecular relaxation, was considered in [25,24,11,1,2] for linear case and in [22] for the nonlinear case.…”

Section: Consider the Nonlinear Third Order Evolutionmentioning

confidence: 99%

Singular Thermal Relaxation Limit for the Moore-Gibson-Thompson Equation Arising in Propagation of Acoustic Waves

Bongarti

Charoenphon

Lasiecka

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Moore-Gibson-Thompson (MGT) equations, which describe acoustic waves in a heterogeneous medium, are considered. These are the third order in time evolutions of a predominantly hyperbolic type. MGT models account for a finite speed propagation due to the appearance of thermal relaxation coefficient τ > 0 in front of the third order time derivative. Since the values of τ are relatively small and often negligible, it is important to understand the asymptotic behavior and characteristics of the model when τ → 0. This is a particularly delicate issue since the τ − dynamics is governed by a generator which is singular as τ → 0. It turns out that the limit dynamics corresponds to the linearized Westervelt equation which is of a parabolic type. In this paper, we provide a rigorous analysis of the asymptotics which includes strong convergence of the corresponding evolutions over infinite horizon. This is obtained by studying convergence rates along with the uniform exponential stability of the third order evolutions. Spectral analysis for the MGT-equation along with a discussion of spectral uppersemicontinuity for both equations (MGT and linearized Westervelt) will also be provided.

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“…to disprove exponential stability. In summary, the analysis carried out in [1] is inconclusive with respect to the open question under consideration.…”

Section: Introductionmentioning

confidence: 99%

A note on the Moore–Gibson–Thompson equation with memory of type II

2019

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We consider the Moore-Gibson-Thompson equation with memory of type IIwhere A is a strictly positive selfadjoint linear operator (bounded or unbounded) and α, β, γ > 0 satisfy the relation γ ≤ αβ. First, we prove a well-posedness result without requiring any restriction on the total mass ̺ of g. Then we show that it is always possible to find memory kernels g, complying with the usual mass restriction ̺ < β, such that the equation admits solutions with energy growing exponentially fast. In particular, this provides the answer to a question raised in [2].2000 Mathematics Subject Classification. 35B35, 35G05, 45D05.

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Moore–Gibson–Thompson equation with memory in a history framework: a semigroup approach

Cited by 36 publications

References 12 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

Singular Thermal Relaxation Limit for the Moore-Gibson-Thompson Equation Arising in Propagation of Acoustic Waves

A note on the Moore–Gibson–Thompson equation with memory of type II

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