A model in one-dimensional thermoelasticity

Cieślak, Tomasz; Galić, Marija; Muha, Boris

doi:10.1016/j.na.2021.112703

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…Only in a few papers this crucial property of the temperature is proven. What is more important, none of the problems describes the thermo‐visco‐elastic model in three dimensional space with the additional nonlinear term in the equation of motion (see previous studies 10,16,17 ). The majority of articles that consider inelastic deformations do not analyze the non‐negativity of the temperature at all, as can be observed in previous works 7,8,18–25 …”

Section: Introductionmentioning

confidence: 99%

On a thermo‐visco‐elastic model with nonlinear damping forces andL¹temperature data

Owczarek

Wielgos

2023

Math Methods in App Sciences

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The aim of this paper is to prove the existence of weak solutions to thermo‐visco‐elastic system of equations. In considered problem, the temperature term is included in the elastic constitutive equations (generalized Hooke's law) as well as in describing the evolution of visco‐elastic strain. The main idea of presented proof is to analyze reformulated model, in which visco‐elastic strain (internal variable) is eliminated. For such system of equations, we propose a two‐level Galerkin approximation, which allows us to show a non‐negativity of temperature during the entire deformation process. In order to characterize the weak limits in the nonlinearities occurring in the system at different levels of approximation, the following tools are used: Truncation methods for heat equation proposed in the paper of D. Blanchard [Nonlinear Analysis, 21(10):725‐743, 1993], modified Boccardo‐Gallouët's approach, and Minty‐Browder trick.

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Section: Introductionmentioning

confidence: 99%

On a thermo‐visco‐elastic model with nonlinear damping forces andL¹temperature data

Owczarek

Wielgos

2023

Math Methods in App Sciences

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Global weak solutions in nonlinear 3D thermoelasticity

Cieślak,

Muha,

Trifunović

2023

Calc. Var.

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Global-in-Time Regular Unique Solutions with Positive Temperature to One-Dimensional Thermoelasticity

Michał Bies,

Cieślak

2023

SIAM J. Math. Anal.

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A model in one-dimensional thermoelasticity

Cited by 3 publications

References 16 publications

On a thermo‐visco‐elastic model with nonlinear damping forces andL¹temperature data

On a thermo‐visco‐elastic model with nonlinear damping forces andL¹temperature data

Global weak solutions in nonlinear 3D thermoelasticity

Global-in-Time Regular Unique Solutions with Positive Temperature to One-Dimensional Thermoelasticity

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A model in one-dimensional thermoelasticity

Cited by 3 publications

References 16 publications

On a thermo‐visco‐elastic model with nonlinear damping forces andL1temperature data

On a thermo‐visco‐elastic model with nonlinear damping forces andL1temperature data

Global weak solutions in nonlinear 3D thermoelasticity

Global-in-Time Regular Unique Solutions with Positive Temperature to One-Dimensional Thermoelasticity

Contact Info

Product

Resources

About

On a thermo‐visco‐elastic model with nonlinear damping forces andL¹temperature data

On a thermo‐visco‐elastic model with nonlinear damping forces andL¹temperature data