Math @ Duke
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Publications [#9848] of Mark Bowen
Papers Published
- M. Bowen, J. R. King and J. Hulshof, Anomalous exponents and dipole solutions for the thin film equation,
SIAM J. Appl. Math., (2001), 62:149-179
[ps]
(last updated on 2001/09/08)
Abstract: Also available as Leiden Preprint MI 01-2000.
We investigate similarity solutions of the second kind (in
that
they feature an
anomalous exponent) for a fourth order degenerate diffusion
equation on
the half-line $x\ge0$. These self-similar solutions are
termed dipole
solutions and, using a combination of phase space
analysis and numerical simulations, we numerically construct
trajectories
representing these solutions, at the same time obtaining
broader insight
into
the nature of the four-dimensional phase space. Additional
asymptotic
analysis provides further information concerning the
evolution to
self-similarity.
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