Publications [#9848] of Mark Bowen

Papers Published

  1. 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
    (last updated on 2001/09/08)

    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.