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In this paper, the phenomenon of synchronization in nonlinearly coupled thermoelastic waves is investigated. The existence of a finite-dimensional smooth global attractor $ \mathcal {A}_\alpha $ A α is proven in the natural energy space, where α is the coupling parameter. It is also proved that the coupled thermoelastic wave system can be reduced to a single thermoelastic wave when α tends to infinity. Subsequently, the upper-semicontinuity of their attractors is proven as $ \alpha \to \infty $ α → ∞. These results are ultimately employed to establish the synchronization phenomena for coupled thermoelastic waves. To the best of our knowledge, the synchronization of thermoelastic waves has not been considered before. [ABSTRACT FROM AUTHOR]

In the literature, one can find numerous modifications of Fourier's law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme's stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study a porous thermoelastic system with microtemperature and strong time delay acting on the volume fraction equation. The thermal effect of microtemperature is based on the Lord–Shulman theory (J Mech Phys Solids. 15(5) (1967), 299–309.), while the strong delay is motivated by Makheloufi's et al. recent work (Math Meth Appl Sci. 44 (2021), 6301–6317.). To prove the well‐posedness of the system, lack of exponential stability and the polynomial decay with optimal rate, we use the semigroup theory of linear operators. [ABSTRACT FROM AUTHOR]

We develop the theory of kernel sections of non-autonomous dynamical systems. Under some sufficient conditions, we establish some abstract results on the asymptotically autonomous stability of kernel sections, which suggests that the time-section of a kernel section is asymptotically stable to a global attractor of the autonomous dynamical system. A lattice plate equation with nonlinear damping and non-autonomous forcing is considered as an application. It is shown that the time-section of kernel sections of the non-autonomous lattice plate equations are nonempty, uniformly compact, pullback attracting, and asymptotically stable to a global attractor of the autonomous lattice plate equations. [ABSTRACT FROM AUTHOR]

We study the qualitative and numerical behavior of a thermodiffusion Timoshenko beam with Kelvin–Voigt damping. The model, recently derived by Aouadi $ \rm et al. $ (2019), describes the behavior of a Timoshenko beam with thermodiffusion effects under the classical Fourier's and Fick's laws for heat and mass diffusion transmission, respectively. With the help of the semigroup theory of linear operators, we prove the well posedness of the considered problem. Without assuming the well-known condition of equal wave speeds, it is shown that the associated $ C_0 $-semigroup to the fully viscoelastic system is analytic. Exponential stability and impossibility of localization of the solutions in time are immediate consequences. Two partial viscoelastic systems are shown to be polynomially or exponentially stable. The approach based on the Gearhart–Herbst–Prüss–Huang theorem is used to show the lack of exponential stability, whereas the optimal polynomial decay rate can be shown using the Borichev & Tomilov's Theorem. Finally, we propose a spectral discretization method to prove that the associated discrete energy decays exponentially or polynomially otherwise. [ABSTRACT FROM AUTHOR]

We investigate dynamics of a class of abstract Timoshenko model with damping and source terms. We obtain a abstract Kirchhoff model as a singular limit of the abstract Timoshenko model when a certain coupling parameter $ a $ tends to infinity. Smooth global attractors with finite fractal dimension and exponential attractors are obtained using the recent quasi-stability theory. We conclude the work comparing the abstract Timoshenko model with abstract Kirchhoff model, in the sense of the upper-semicontinuity of their attractors as $ a $ tends to infinite. [ABSTRACT FROM AUTHOR]

This rodent (Wistar rats) study examined reproductive effects of in utero /lactational exposure to a mixture of 6 antiandrogenic phthalates (PMix): diisobutyl phthalate, di- n -butyl phthalate, diisopentyl phthalate, butylbenzyl phthalate, di-2-ethylhexyl phthalate, and diisononyl phthalate. The PMix was defined based on exposure data from pregnant women in Brazil. Experimental groups were established by extrapolating the estimated human dose to rats (0.1 mg/kg/day), followed by up to 3 additional doses corresponding to 5, 1000, and 5000 times the starting rat dose: 0 (control), 0.1, 0.5, 100, and 500 mg/kg/day. The fetal experiment assessed gestational exposure effects on fetal gonads, whereas the postnatal experiment evaluated reproductive parameters in males and females after in utero and lactational exposure. Prenatal exposure decreased fetal testicular testosterone production at 0.5 and 500 mg/kg/day. PMix 500 also reduced mRNA expression of steroidogenesis-related genes, upregulated transcript expression of the retinoic acid-degrading enzyme Cyp26b1 , and increased multinucleated gonocytes incidence in fetal testes. Postnatal assessment revealed antiandrogenic effects at the highest dose, including reduced anogenital distance, nipple retention, and decreased weight of reproductive organs. Early puberty onset (preputial separation) was observed at the lowest dose in males. In contrast, females did not show significant changes in fetal and adult endpoints. Overall, the PMix recapitulated early and late male rat phthalate syndrome phenotypes at the highest dose, but also induced some subtle changes at lower doses, which warrant confirmation and mechanistic assessments. Our data support the use of epidemiologically defined mixtures for exposure risk assessments over traditional toxicological approaches. [ABSTRACT FROM AUTHOR]

This paper targets the long-time dynamics of a semilinear system modeling a binary mixture of solids with frictional dissipation mechanism acting only on the elastic equation and subjected to nonlinear source term. The coupling gives new contributions to the theory associated with nonlinear dynamics of partially damped semilinear systems of a binary mixture of solids. Using the quasi-stability methods, we prove the existence of a smooth finite-dimensional global attractor irrespective of the wave speeds of the system. Moreover, we establish the existence of exponential attractors. [ABSTRACT FROM AUTHOR]