Asymptotic behavior of α-entropy solutions to the thin film equation on the sphere

We investigate the existence and behavior of α -entropy solutions to the double-degenerate thin-film equation, which models viscous coating flows on spherical surfaces. Our results show that these solutions exhibit both finite-speed propagation and a waiting-time phenomenon. Furthermore, we derive an upper bound for the interface propagation rate and a lower bound for the waiting time. Numerical simulations are also presented to support the analytical results.