Convergence to equilibrium for a thin film equation on a cylindrical surface

Details Convergence to equilibrium for a thin film equation on a cylindrical surface Convergence to equilibrium for a thin film equation on a cylindrical surface

2010-11-09

arxiv.org/abs/1011.2108v2

Mathematics

Analysis of PDEs

26 pages, 6 figures. This is a greatly expanded version of our previous submission [arXiv:1009.4092v1]. The main result on con

Scientific paper

The degenerate parabolic equation u_t + [u^3(u_xxx + u_x - sin x)]_x=0 models the evolution of a thin liquid film on a stationary horizontal cylinder. It is shown here that for each given mass there is a unique steady state, given by a droplet hanging from the bottom of the cylinder that meets the dry region at the top with zero contact angle. The droplet minimizes the energy and attracts all strong solutions that satisfy certain energy and entropy inequalities. The distance of any solution from the steady state decays no faster than a power law.

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