arXiv:2212.02262 Abstract | arXiv Analytics

arXiv:2212.02262 [math.AP]Abstract References Reviews Resources

Invariant Manifolds for the Thin Film Equation

Published 2022-12-05Version 1

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.

Categories: math.AP

Keywords: thin film equation, finite-dimensional invariant manifolds, self-similar smyth-hill solutions, higher order asymptotics, linear mobility

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