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arXiv · 2212.02262

Invariant Manifolds for the Thin Film Equation

Christian Seis·Dominik Winkler
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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.

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Christian Seis, Dominik Winkler. 2022-12-05. Invariant Manifolds for the Thin Film Equation. https://arxiv.org/abs/2212.02262

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