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The penetration of a monotonically time-increasing magnetic field in high-temperature superconductors (HTSC) slabs with the power law dependencies of the critical current density and resistivity on the magnetic field is investigated theoretically. It is shown that the asymptotic solutions of the extended critical state model correspond to the cases of the classical critical state model and the model of viscous flux flow without pinning. The ranges of the applicability of these models and the conditions for the transition from one model to the other are determined. These theoretical conclusions explain experimental data presented in scientific literature.