Invariant Manifolds for the Thin Film Equation

Abstract

The large-time behavior of solutions to the thin film equation with linear mobility in the complete wetting regime on \(\mathbb {R}^N\) is examined. We investigate the higher order asymptotics of solutions converging towards self-similar Smyth–Hill solutions under certain symmetry assumptions on the initial data. The analysis is based on a construction of finite-dimensional invariant manifolds that solutions approximate to an arbitrarily prescribed order.