Intermediate asymptotics of the capillary-driven thin-film equation
Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI, Paris, France
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Accepted: 10 June 2013
Published online: 9 August 2013
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.
Key words: Flowing Matter: Interfacial phenomena
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2013