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Eur Phys J E Soft Matter. 2013 Aug;36(8):82. doi: 10.1140/epje/i2013-13082-3. Epub 2013 Aug 9.

Intermediate asymptotics of the capillary-driven thin-film equation.

Author information

1
Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, Paris, France.

Abstract

We present an analytical and numerical study of the two-dimensional capillary-driven thin-film equation. In particular, we focus on the intermediate asymptotics of its solutions. Linearising the equation enables us to derive the associated Green's function and therefore obtain a complete set of solutions. Moreover, we show that the rescaled solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the rescaled Green's function. Finally, a numerical study on compact-support initial profiles enables us to conjecture the extension of our results to the nonlinear equation.

PMID:
23921450
DOI:
10.1140/epje/i2013-13082-3
[Indexed for MEDLINE]

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