Initial-boundary value problem with a free surface condition for the penalized equations of aqueous solutions of polymers

The existence “in a small” of the solutions of the perturbed initialboundary value problems (1), (2) and (2), (3) is proved. The convergence for $\varepsilon\to0$ of the solutions $\{v^\varepsilon\}$ of these problems to the solution of the initial-boundary value problem (4), (3) for the equations of aqueous solutions of polymers (4) is investigated. Bibliography: 10 titles.