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In this work, we consider initial-boundary-value problems for motion equations of a viscoelastic medium with the Jeffreys constitutive law and for motion equations of the regularized Jeffreys model. We obtain a theorem on the convergence of weak solutions of initial-boundary-value problems for the regularized model to weak solutions of the original problem as the regularization parameter tends to zero.

On the convergence of solutions of the regularized problem for motion equations of Jeffreys viscoelastic medium to solutions of the original problem