The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Interfaces and Free Boundaries


Full-Text PDF (135 KB) | Metadata | Table of Contents | IFB summary
Volume 4, Issue 3, 2002, pp. 309–323
DOI: 10.4171/IFB/63

Published online: 2002-09-30

Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case

Günther Grün[1]

(1) Universität Erlangen-Nünberg, Germany

We prove optimal estimates on the growth rate of the support of solutions to the thin-film equation ut + div(|u|n[nabla] [Dgr]u) = 0 in space dimensions N = 2 and N = 3 for parameters n [isin] [2, 3) which correspond to Navier's slip condition (n = 2) or certain variants modeling weaker slippage effects. Our approach relies on a new class of weighted energy estimates. It is inspired by the onedimensional technique of Hulshof and Shishkov Adv. Diff. Equations 3, (1998) 625-642, and it simplifies their method, mainly with respect to basic integral estimates to be used.

Keywords: fourth-order degenerate parabolic equations; finite speed of propagation; thin films

Grün Günther: Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case. Interfaces Free Bound. 4 (2002), 309-323. doi: 10.4171/IFB/63