Math @ Duke
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Publications [#9846] of Mark Bowen
Papers Published
- J. R. King and M. Bowen, Moving boundary problems and non-uniqueness for the thin film equation,
Euro. J. Appl. Math. (2001), 12:321-356
[ps]
(last updated on 2001/09/07)
Abstract: Also avalaiable as Leiden preprint MI 28-99.
A variety of mass preserving moving boundary problems for
the thin film
equation, $u_{t}=-(u^{n}u_{xxx})_{x}$, are derived (by
formal asymptotics)
from a number of regularisations, the case in which the
substrate is
covered by a very thin pre-wetting film being discussed in
most detail.
Some of the properties of the solutions selected in this
fashion are
described and the full range of possible mass preserving
non-negative
solutions is outlined.
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