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math.AP2026

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

Michael Winkler

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…

math.AP2025

Large-data solutions in one-dimensional thermoviscoelasticity involving temperature-dependent viscosities

Michael Winkler

An initial-boundary value problem for \[ \left\{ \begin{array}{ll} u_{tt} = \big(γ(Θ) u_{xt}\big)_x + au_{xx} - \big(f(Θ)\big)_x, \qquad & x\inΩ, \ t>0, \\[1mm] Θ_t = Θ_{xx}…

math.AP2025

Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities

Michael Winkler

The model \[ \left\{ \begin{array}{l} u_{tt} = \big(γ(Θ) u_{xt}\big)_x + au_{xx} - \big(f(Θ)\big)_x, \\[1mm] Θ_t = Θ_{xx} + γ(Θ) u_{xt}^2 - f(Θ) u_{xt}, \end{array} \right.…