Thermoelastic problem in the setting of dual-phase-lag heat conduction: Existence and uniqueness of a weak solution

Maes, Frederick; Bockstal, Karel Van

doi:10.1016/j.jmaa.2021.125304

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…Therefore, Tzou [3][4] attributed the entire effect of the microstructure to the delay of the macroscopic equation, the dual-phase-lagging (DPL) model is proposed. Maes et al [5] investigated an isotropic thermoelastic system with the DPL heat conduction. They consider a homogeneous Dirichlet boundary condition for displacement and temperature and formulate the variational formulation for the associated fully hyperbolic coupled system.…”

Section: Introductionmentioning

confidence: 99%

Singularly Perturbed Solution of Non-Fourier Temperature Field with Mixed Boundary Value Dual-Phase Delay with Thermal Conductivity Jumps

Li-ping

Jiang

2022

J. Phys.: Conf. Ser.

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Based on the properties of laminates, a class of nonlinear singularly perturbed mixture equations with discontinuous coefficients over bounded domains is constructed by using a dual-phase delayed heat conduction model. First, the singular perturbation expansion method is used, combined with the corresponding boundary conditions, the partial differential equation method and the Laplace transform method are used to obtain the external solution, the boundary layer, and the corner layer. Secondly, the time-varying temperature field at the discontinuity is obtained, which leads to the asymptotic expansion of the solution. Finally, the consistent validity of the asymptotic solution is obtained through residual estimation.

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Section: Introductionmentioning

confidence: 99%

Singularly Perturbed Solution of Non-Fourier Temperature Field with Mixed Boundary Value Dual-Phase Delay with Thermal Conductivity Jumps

Li-ping

Jiang

2022

J. Phys.: Conf. Ser.

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On Inverse Source Problems for Space-Dependent Sources in Thermoelasticity

Maes,

Van Bockstal

2024

Trends in Mathematics

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A dual-phase-lag porous-thermoelastic problem with microtemperatures

Bazarra

Fernández

Quintanilla³

2022

era

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<abstract><p>In this work, we consider a multi-dimensional dual-phase-lag problem arising in porous-thermoelasticity with microtemperatures. An existence and uniqueness result is proved by applying the semigroup of linear operators theory. Then, by using the finite element method and the Euler scheme, a fully discrete approximation is numerically studied, proving a discrete stability property and a priori error estimates. Finally, we perform some numerical simulations to demonstrate the accuracy of the approximation and the behavior of the solution in one- and two-dimensional problems.</p></abstract>

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Thermoelastic problem in the setting of dual-phase-lag heat conduction: Existence and uniqueness of a weak solution

Cited by 3 publications

References 25 publications

Singularly Perturbed Solution of Non-Fourier Temperature Field with Mixed Boundary Value Dual-Phase Delay with Thermal Conductivity Jumps

Singularly Perturbed Solution of Non-Fourier Temperature Field with Mixed Boundary Value Dual-Phase Delay with Thermal Conductivity Jumps

On Inverse Source Problems for Space-Dependent Sources in Thermoelasticity

A dual-phase-lag porous-thermoelastic problem with microtemperatures

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