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

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.