We investigate the non-linear dynamics of a two-dimensional film flowing downa finite heater, for a non-volatile and a volatile liquid. An oscillatoryinstability is predicted beyond a critical value of Marangoni number usinglinear stability theory. Continuation along the Marangoni number usingnon-linear evolution equation is used to trace bifurcation diagram associatedwith the oscillatory instability. Hysteresis, a characteristic attribute of asub-critical Hopf bifurcation, is observed in a critical parametric region. Thebifurcation is universally observed for both, a non-volatile film and avolatile film.
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