  Motivated by a model proposed by Peng et al. [Advances in Coll. and Interf.
Sci. 206 (2014)] for break-up of tear films on human eyes, we study the
dynamics of a generalized thin film model. The governing equations form a
fourth-order coupled system of nonlinear parabolic PDE for the film thickness
and salt concentration subject to non-conservative effects representing
evaporation. We analytically prove the global existence of solutions to this
model with mobility exponents in several different ranges and the results are
then validated against PDE simulations. We also numerically capture other
interesting dynamics of the model, including finite-time rupture-shock
phenomenon due to the instabilities caused by locally elevated evaporation
rates, convergence to equilibrium and infinite-time thinning.
