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| Publications [#9864] of Thomas P. Witelski
search www.ams.org.Papers Published
- A. L. Bertozzi, G. Grun, Thomas P. Witelski, Dewetting films: bifurcations and concentrations,
Nonlinearity, 14 (2001) pp 1569--1592
(last updated on 2001/12/11)
Abstract:
Under the influence of long range attractive and short range
repulsive forces,
thin liquid films rupture and form complex dewetting
patterns.
This paper studies this phenomenon in one space dimension in
the framework
of fourth order degenerate parabolic equations of
lubrication type.
We derive the global structure of the bifurcation
diagram for steady state solutions.
A stability analysis of the solution branches and numerical
simulations
suggest coarsening occurs.
Furthermore, we study the behavior of solutions in the limit
that short range repulsive forces are neglected. Both
asymptotic analysis and
numerical
experiments show that this limit can concentrate mass in
$\delta$-distributions.
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