Intermediate asymptotics of the capillary-driven thin-film equation

@article{Benzaquen2012IntermediateAO,
  title={Intermediate asymptotics of the capillary-driven thin-film equation},
  author={Michael Benzaquen and Thomas J Salez and {\'E}lie Rapha{\"e}l},
  journal={The European Physical Journal E},
  year={2012},
  volume={36},
  pages={1-7}
}
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… 
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