The asymptotic solution of a class of third-order boundary value problems arising in the theory of thin film flows

This paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third-order boundary value problems which govern the motion of thin liquid films subject to viscous, capillary and gravitational forces. Precise conditions specifying where and when the third-order derivative terms in the differential equations can be neglected are derived, and improved estimates for the actual solutions in terms of solutions of the lower-order models are constructed. The paper also contains a technique for replacing a third-order problem with an asymptotically equivalent second-order one that may have wider applicability.