Hotspot Formation Driven by Temperature-Dependent Coefficients in One-Dimensional Thermoviscoelasticity

Abstract

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 [Formula: see text] norm in the temperature variable is discovered.