Lord–Shulman Thermoelasticity with Microtemperatures

Bazarra, Noelia; Quintanilla, R.

doi:10.1007/s00245-020-09691-2

Cited by 28 publications

(26 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Hence, in this work we continue the research started in [44]. We introduce a fully discrete approximation by using the finite element method and the implicit Euler scheme, we prove a discrete stability property, we obtain a priori error estimates, from which the linear convergence of the approximation is derived under suitable regularity conditions, and we perform some numerical simulations in one and two dimensions.…”

Section: Introductionmentioning

confidence: 93%

“…In this section, we present the mathematical model, we derive its variational formulation and we state an existence and uniqueness result (see [44]).…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

“…According to [44], for isotropic and homogeneous materials the system of equations becomes, in Ω × (0, T f ) and for i = 1, . .…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

“…Therefore, it is natural to ask ourselves by the rate of decay of the solutions. In the reference [44] we analyzed this aspect for the one-dimensional case and we proved (by means of the semigroup arguments) that the solutions decay in an exponential way. That is, the energy of the system can be controlled by an exponential function.…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

“…It is worth noting that this system was studied in a qualitative way in a recent paper [44]. It was obtained existence and stability results.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

2020

Self Cite

View full text Add to dashboard Cite

In this paper we deal with the numerical analysis of the Lord-Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness result is stated. Then, a fully discrete approximation is introduced using the finite element method and the implicit Euler scheme. A discrete stability property is shown, and an a priori error J. Baldonedo acknowledges the funding by Xunta de Galicia (Spain) under the program Axudasá etapa predoutoral with Ref.

show abstract

Section: Introductionmentioning

confidence: 93%

“…In this section, we present the mathematical model, we derive its variational formulation and we state an existence and uniqueness result (see [44]).…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

“…According to [44], for isotropic and homogeneous materials the system of equations becomes, in Ω × (0, T f ) and for i = 1, . .…”

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

Section: The Model and Its Variational Formulationmentioning

confidence: 99%

“…It is worth noting that this system was studied in a qualitative way in a recent paper [44]. It was obtained existence and stability results.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

2020

Self Cite

View full text Add to dashboard Cite

show abstract

Well posedness and stability result of Lord–Shulman system with microtemperature effects: The case ξμ∗=μ02

Boudeliou,

Djebabla,

Apalara

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In this study, we investigate the Lord–Shulman porous elastic system with dissipation caused by the microtemperature effects. Here, the thermal conduction has a single‐phase‐lag that acts as a relaxation time and the energy associated with the solution is not required to be positive definite . We introduce a stability number and prove using the multiplier technique that the exponential decay of the system is valid if . Otherwise, we show that the system decays polynomially.

show abstract

Polynomial stability for Lord–Shulman porous elasticity with microtemperature and strong time delay

Ramos,

Araujo,

Freitas

et al. 2024

Z Angew Math Mech

View full text Add to dashboard Cite

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.

show abstract

Lord–Shulman Thermoelasticity with Microtemperatures

Abstract: Portal del coneixement obert de la UPC http://upcommons.upc.edu/e-prints This is a post-peer-review, pre-copy edit version of an article published in A p p l i e d m a t h e m a t i c s a n d o p t i m i z a t i o n . The

Cited by 28 publications

References 41 publications

An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

Well posedness and stability result of Lord–Shulman system with microtemperature effects: The case ξμ∗=μ02

Polynomial stability for Lord–Shulman porous elasticity with microtemperature and strong time delay

Contact Info

Product

Resources

About