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arXiv · 1708.00243

Self-similar lifting and persistent touch-down points in the thin-film equation

Carlota M. Cuesta·Hans Knüpfer·Juan J. L. Velázquez
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Abstract

We study self-similar solutions of the thin-film equation, with mobility exponent m in (0,4], that describe the lifting of an isolated touch-down point given by an initial profile of the form |x|. This provides a mechanism for non-uniqueness of the thin-film equation with m in (2,4), since solutions with a persistent touch-down point also exist in this case. In order to prove existence of the self-similar solutions, we need to study a four-dimensional continuous dynamical system. The proof consists of a shooting argument based on the identification of invariant regions and on suitable energy formulas.

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Carlota M. Cuesta, Hans Knüpfer, Juan J. L. Velázquez. 2017-08-01. Self-similar lifting and persistent touch-down points in the thin-film equation. https://arxiv.org/abs/1708.00243

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