To describe the functioning of pulsating heat pipe, one needs to understand the dynamics of evaporation of thin liquid films deposited by the oscillating meniscus inside a heated capillary. Following the theory of Taylor bubbles, the dynamic profile of the liquid-vapor interface is calculated within a 2D numerical approach using the lubrication approximation. First, the steady vicinity of the contact line is analyzed under evaporation for the partial wetting case to find a relation between the microscopic and apparent contact angles. Next, the film evolution driven by the oscillating meniscus with a pinned contact line is discussed under adiabatic conditions. Finally, the evaporation of oscillating film is considered. It is shown that the film oscillation with a pinned contact line is impossible when the capillary superheating exceeds a threshold; the contact line receding needs to be taken into consideration.