Hotspot formation driven by temperature-dependent coefficients in one-dimensional thermoviscoelasticity

Michael Winkler

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arXiv · 2602.03997

Hotspot formation driven by temperature-dependent coefficients in one-dimensional thermoviscoelasticity

Michael Winkler

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Abstract

This manuscript is concerned with a two-component evolution system generalizing the classical model for one-dimensional thermoviscoelastic dynamics in Kelvin-Voigt materials in the presence of temperature-dependent viscosities and elastic stiffnesses. Under suitable assumptions on the growth of these ingredients and on the initial data, the occurrence of finite-time blow-up with respect to the $L^\infty$ norm in the temperature variable is discovered.

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Michael Winkler. 2026-02-03. Hotspot formation driven by temperature-dependent coefficients in one-dimensional thermoviscoelasticity. https://arxiv.org/abs/2602.03997

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