  In order to investigate the emergence of periodic oscillations of rimming
flows, we study analytically the stability of steady states for the model of
(Benilov, Kopteva, O'Brien, 2005), which describes the dynamics of a thin fluid
film coating the inner wall of a rotating cylinder and includes effects of
surface tension, gravity, and hydrostatic pressure. We apply multi-parameter
perturbation methods to eigenvalues of Fr\'echet derivatives and prove the
transition of a pair of conjugate eigenvalues from the stable to the unstable
complex half-plane under appropriate variations of parameters. In order to
prove rigorously the corresponding branching of periodic solutions from
critical equilibria, we extend the multi-parameter Hopf-bifurcation theory to
the case of infinite-dimensional dynamical systems.
