Stability of abstract thermoelastic systems with inertial terms

Sare, Hugo D. Fernández; Liu, Zhuangyi; Racke, Reinhard

doi:10.1016/j.jde.2019.07.015

Cited by 13 publications

(9 citation statements)

References 25 publications

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“…In the full space Ω = R d , the well-posedness and decay rates have also been established -both in the linear [46] and the nonlinear cases [47]. A recent systematic study [14] on abstract fractional-power thermoelastic plate systems should also be mentioned.…”

Section: In Bounded Domainsmentioning

confidence: 99%

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

2019

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We consider an initial-boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell-Cattaneo-Vernotte law giving rise to a 'second sound' effect. We study the local wellposedness of the resulting quasilinear mixed-order hyperbolic system in a suitable solution class of smooth functions mapping into Sobolev H k -spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small in a lower topology (basic energy level corresponding to weak solutions), we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.

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Section: In Bounded Domainsmentioning

confidence: 99%

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

2019

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“…See [14] for a simpler system. -The semigroup properties obtained in [8] and this paper provides important information for the study of nonlinear evolution equations related to the linear system (1.1). -The asymptotic analysis of eigenvalues for system (1.1) is crucial to precisely divide the parameter region E into subregions corresponding to the semigroup properties.…”

Section: Resultsmentioning

confidence: 76%

“…(b) By a detailed spectral analysis, we will show that the orders of Gevrey class is sharp, under proper conditions. (c) We also show that the orders of polynomial stability obtained in [8] are optimal.…”

Section: The Semigroupmentioning

confidence: 73%

“…It is known that A α,β,γ generates a C 0 -semigroup e A α,β,γ t of contractions on H, see [8]. Then the solution to the evolution equation (1.2) admits the following representation:…”

Section:     mentioning

confidence: 99%

“…How to prove these properties in each subregion? Recently, the stability analysis of the system (1.1) has been reported in [8]. For reader's convenience, we give a brief summary here.…”

Section: Semigroup Ementioning

confidence: 99%

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Regularity analysis for an abstract thermoelastic system with inertial term

2021

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In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations. The asymptotic stability of this model was investigated in [6]. We are able to decompose the parameter region into three parts where the semigroup associated with the system is analytic, of Gevrey class of specific order, and non-smoothing, respectively. Moreover, by a detailed and creative spectral analysis,, we will show that the order of Gevrey class is sharp, under proper conditions. We also show that the orders of the polynomial stability obtained in [6] is optimal.

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Stability and regularity for double wall carbon nanotubes modeled as Timoshenko beams with thermoelastic effects and intermediate damping

Sobrado Suárez,

Barbosa Sobrado,

de Araujo

et al. 2024

Math Methods in App Sciences

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This research studies two systems composed by the Timoshenko beam model for double‐wall carbon nanotubes, coupled with the heat equation governed by Fourier's law. For the first system, the coupling is given by the rotation speed of the vertical filament in the beam from the first beam of Timoshenko and the Laplacian of temperature , where we also consider the damping terms fractionals , , and , where . For this first system, we proved that the semigroup associated to system decays exponentially for all . The second system also has three fractional dampings , , and , with . Furthermore, the couplings between the heat equation and the Timoshenko beams of the double wall carbon nanotubes for the second system are given by the Laplacian of the rotation speed of the vertical filament in the beam of the first beam of Timoshenko and the Lapacian of temperature . For the second system, we prove the exponential decay of the associated semigroup for and also show that this semigroup admits Gevrey classes for , and we finish our investigation proving that is analytic when the parameters .

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Stability of abstract thermoelastic systems with inertial terms

Cited by 13 publications

References 25 publications

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

Long-time behavior of quasilinear thermoelastic Kirchhoff–Love plates with second sound

Regularity analysis for an abstract thermoelastic system with inertial term

Stability and regularity for double wall carbon nanotubes modeled as Timoshenko beams with thermoelastic effects and intermediate damping

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