Papers Published
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.