On two-scale homogenized equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth data☆

We study the initial-boundary value problem for a system of quasilinear equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth coefficients and initial data. We rigorously justify the passage to the corresponding limit initial-boundary value problem for a system of two-scale homogenized integro-differential equations, including the existence theorem for the limit problem. The results are global with respect to the time interval and the data.