The initial boundary value problem for Kelvin–Voigt type viscoelasticity model with frame–indifferent constitutive law with regularized objective Yaumann derivative and with infinite memory is considered. A weak solvability of the initial boundary value problem is established. The research is based on the approximation-topological method. For this purpose, we consider an approximating sequence of regularized problems over finite time intervals, for which weak solvability and uniform w.r.t. approximation parameter estimates of weak solutions are established. These estimates allow us to perform passage to the limit in approximating problems.
Zvyagin et al. (Sat,) studied this question.