Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models

Badal R, Friedrich M, Kružík M, Machill L (2025)

Publication Type: Journal article

Publication year: 2025

Journal

Journal De Mathematiques Pures Et Appliquees Elsevier

Book Volume: 202

Article Number: 103751

DOI: 10.1016/j.matpur.2025.103751

Abstract

According to the Nernst theorem or, equivalently, the third law of thermodynamics, the absolute zero temperature is not attainable. Starting with an initial positive temperature, we show that there exist solutions to a Kelvin-Voigt model for quasi-static nonlinear thermoviscoelasticity at a finite-strain setting [45], obeying an exponential-in-time lower bound on the temperature. Afterwards, we focus on the case of deformations near the identity and temperatures near a critical positive temperature, and we show that weak solutions of the nonlinear system converge in a suitable sense to solutions of a system in linearized thermoviscoelasticity. Our result extends the recent linearization result in [4], as it allows the critical temperature to be positive.

Authors with CRIS profile

Rufat Badal Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik) Manuel Friedrich Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Institute of Information Theory and Automation (UTIA)

Czech Republic (CZ) Rheinische Friedrich-Wilhelms-Universität Bonn

Germany (DE)

How to cite

APA:

Badal, R., Friedrich, M., Kružík, M., & Machill, L. (2025). Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models. Journal De Mathematiques Pures Et Appliquees, 202. https://doi.org/10.1016/j.matpur.2025.103751

MLA:

Badal, Rufat, et al. "Positive temperature in nonlinear thermoviscoelasticity and the derivation of linearized models." Journal De Mathematiques Pures Et Appliquees 202 (2025).

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