Michael Benzaquen, Thomas Salez, Élie Raphaël
We present an analytical and numerical study of the two-dimensional capillary-driven thin film equation. In particular, we focus on the 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 solution for any summable initial profile uniformly converges in time towards a universal self-similar attractor that is precisely the Green's function multiplied by the initial algebraic volume. Finally, a numerical study enables us to conjecture the extension of our results to the nonlinear equation.
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http://arxiv.org/abs/1211.7301
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