Finite speed of propagation for thin viscous flows over an inclined plane

In this paper, we consider the fourth-order nonlinear degenerate parabolic equation ht+[hn(hxxx−αhx+β)]x=0,ht+[hn(hxxx−αhx+β)]x=0, which arises in lubrication models for thin viscous flows over an inclined plane. It is shown that if 43≤n<2 this equation has finite speed of propagation property for the nonnegative strong solutions. The upper bound for the speed of the support of this solution is obtained. Our approach is based on a perturbation method combined with the local energy/entropy method.