Long-time dynamics of an extensible plate equation with thermal memory

Barbosa, Alisson Rafael Aguiar; Fu, To

doi:10.1016/j.jmaa.2014.02.042

Cited by 63 publications

(44 citation statements)

References 24 publications

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“…Author details 1 Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Pullback attractor for N-dimensional thermoelastic coupled structure equations

Wang

2018

Bound Value Probl

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In this paper, proving the pullback asymptotic compactness of processes by the aid of a contractive function in space X 0 , we prove the existence of a pullback attractor for N-dimensional nonautonomous thermoelastic coupled structure equationswith the lateral load distribution function h(x, t) and the external heat supply function q(x, t) unnecessarily bounded. The nonlinear source term g(u) is essentiallyif N ≥ 3 and 1 < ρ < ∞ if N = 1, 2.

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“…Author details 1 Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, P.R. China.…”

Section: Competing Interestsmentioning

confidence: 99%

Pullback attractor for N-dimensional thermoelastic coupled structure equations

Wang

2018

Bound Value Probl

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“…We note that assumption γ 0 = c = 0 was used in [4,13,18,29] for several different plate models with thermal memory. Therefore by re-normalizing coefficients and assuming that f 1 = f (w) we obtain our system (1.2)-(1.3) in the case of ω = 0.…”

Section: Justification Of the Thermoelastic Modelmentioning

confidence: 99%

“…5]). These systems were studied in, e.g., [4,14,18,19,29,33]. Therefore problem (1.2)-(1.3) can be viewed as a p-Laplacian perturbation of known thermoelastic models.…”

Section: Introductionmentioning

confidence: 99%

Long-time behavior of a class of thermoelastic plates with nonlinear strain

Fatori

Silva

et al. 2015

Journal of Differential Equations

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In recent years a class of vibrating plates with nonlinear strain of p-Laplacian type was studied by several authors. The present paper contains a first thermoelastic model of that class of problems including both Fourier and non-Fourier heat laws. Our main result establishes the existence of global and exponential attractors for the strongly damped problem through a stabilizability inequality. In addition, for the weakly damped problem, we establish the exponential stability of its Galerkin semiflows.

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“…The case of = ≡ 0 in problem (1) has been studied by several authors (see [2,5,[15][16][17][18][19][20][21][22][23] and references therein). For instance, Wu [15] scrutinized the existence of global attractors for the nonlinear plate equation with thermal memory effects due to non-Fourier heat flux laws when ( ) = −Δ .…”

Section: Introductionmentioning

confidence: 99%