Geodesic
Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case
Günther Grün1
1Universität Erlangen-Nünberg, Germany
Interfaces and free boundaries, Tome 4 (2002) no. 3, pp. 309-323

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DOI

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.
DOI : 10.4171/ifb/63
Classification : 46-XX, 60-XX
Mots-clés : fourth-order degenerate parabolic equations; finite speed of propagation; thin films

Günther Grün  1

1 Universität Erlangen-Nünberg, Germany 
Günther Grün. Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case. Interfaces and free boundaries, Tome 4 (2002) no. 3, pp. 309-323. doi: 10.4171/ifb/63
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     journal = {Interfaces and free boundaries},
     pages = {309--323},
     year = {2002},
     volume = {4},
     number = {3},
     doi = {10.4171/ifb/63},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/63/}
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