For a pair of liquids with contrast mobility a reduced model of flow with phase transitions is proposed, which makes possible an effective qualitative research. It is shown, that the model problem of flow to a single drain is singularly perturbed and can be solved in the analytical way by a matching asymptotic method. The nature of the singularity is associated with violation of a contrast flow condition in some zones. It is shown that the solution can be unstable, depending on the direction of the inter-phase mass exchange and on the flow zone.
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