- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:02
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
4
2002
3
Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case
Günther
Grün
Universität Erlangen-Nünberg, ERLANGEN, GERMANY
fourth-order degenerate parabolic equations; finite speed of propagation; thin films
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.
Functional analysis
Probability theory and stochastic processes
309
323
10.4171/IFB/63
http://www.ems-ph.org/doi/10.4171/IFB/63