Global existence and numerical simulations for a thermoelastic diffusion problem in moving boundary

Madureira, Rodrigo L. R.; Rincon, Mauro A.; Aouadi, Moncef

doi:10.1016/j.matcom.2019.07.001

Cited by 7 publications

(2 citation statements)

References 16 publications

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“…The proof of the existence and uniqueness of the problem ( 1) and ( 2) can be found in [7], where the Lions [8] penalty method was used. For the completeness of this work, we have included all the details related to the estimates, crossing the limit and uniqueness, using the Faedo-Galerkin method.…”

Section: Analytical Resultsmentioning

confidence: 99%

“…In this paper, different from the article [5], although also linear, we present a model for thermal diffusion in elastic body containing a hyperbolic and two parabolic equations. We work with moving boundary and this type of problem is based on a suitable change of space variable which allows transforming the problem into another initial boundary value problem in a fixed domain, that is, with time-independent cross sections (see for instance [6,7]).…”

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confidence: 99%

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Numerical methods for a problem of thermal diffusion in elastic body with moving boundary

Madureira

Rincon

Teixeira

2021

Numerical Methods Partial

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Coupled parabolic-hyperbolic system often appears in the studies of thermoelasticity, magnetoelasticity, biological problems and radiation hydrodynamics with high temperature. In this paper, we investigate a problem of thermal diffusion in elastic body with moving boundary. Three numerical methods, two uncoupled and one coupled, all with quadratic convergence order in time and space, are presented and compared in relation to the execution time. Tables and figures of the approximate solution are shown to verify the efficiency and feasibility of the proposed method. In addition, we show that the numerical results are consistent with the theoretical results. The approximate numerical solutions are calculated using the finite element method in spatial variable and finite difference method in time. To compare different numerical schemes, we show the convergence rates through numerical simulations with calculated error and the execution time. KEYWORDScoupled and uncoupled method, finite elements method, moving boundary, numerical simulation, thermal diffusion INTRODUCTIONThe thermal diffusion in elastic body is governed by a coupled system of hyperbolic-parabolic equations. In [1], the theory was developed using the coupled thermoelastic model. Uniqueness and reciprocity theorems for the generalized problem of thermal diffusion in elastic body in isotropic media, was proved in [2], under restrictive assumptions on the elastic coefficients. In these works, one

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Section: Analytical Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Numerical methods for a problem of thermal diffusion in elastic body with moving boundary

Madureira

Rincon

Teixeira

2021

Numerical Methods Partial

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Dynamics of a nonlinear laminated beam with thermodiffusion effects

Li,

Feng

2023

Math Methods in App Sciences

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A laminated beam system with thermodiffusion effects is considered. The main result is the long‐time dynamics of the system. By showing the system is gradient and asymptotic smoothness, the existence of a global attractor is obtained, which is characterized as unstable manifold of the set of stationary solutions. The quasi‐stability of the system and the finite fractal dimension of the global attractor are established by a stabilizability inequality. The continuity of global attractors regarding the parameter in a residual dense set is finally proved.

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Attractors of a thermoelastic Bresse system with mass diffusion

Li,

Cabanillas,

Feng

2024

Z Angew Math Mech

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This paper concerns the long‐time dynamics of a thermoelastic Bresse system with mass diffusion. We prove the existence of a global attractor by showing that the system is gradient and asymptotically smooth. In addition, the attractor is characterized as an unstable manifold of the set of stationary solutions. The quasi‐stability of the system and the finite fractal dimension of the global attractor are established by a stabilizability inequality. Finally, we prove the upper semicontinuity of the global attractor regarding the parameter in a dense residual set.

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Global existence and numerical simulations for a thermoelastic diffusion problem in moving boundary

Cited by 7 publications

References 16 publications

Numerical methods for a problem of thermal diffusion in elastic body with moving boundary

Numerical methods for a problem of thermal diffusion in elastic body with moving boundary

Dynamics of a nonlinear laminated beam with thermodiffusion effects

Attractors of a thermoelastic Bresse system with mass diffusion

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