  Existence of non-negative weak solutions is shown for a full curvature
thin-film model of a liquid thin film flowing down a vertical fibre. The proof
is based on the application of a priori estimates derived for energy-entropy
functionals. Long-time behaviour of these weak solutions is analysed and, under
some additional constraints for the model parameters and initial values,
convergence towards a travelling wave solution is obtained. Numerical studies
of energy minimizers and travelling waves are presented to illustrate
analytical results.
