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| Publications [#22790] of Thomas P. Witelski
search www.ams.org.Papers Published
- Thomas P. Witelski and Andrew J. Bernoff and Andrea L. Bertozzi, Blowup and dissipation in a critical-case unstable thin film equation,
European Journal of Applied Mathematics, vol. 15 no. 2
(April, 2004),
pp. 223-256
(last updated on 2004/06/08)
Abstract:
We study the dynamics of dissipation and
blow-up in a
critical-case unstable thin film equation.
The governing
equation is a nonlinear fourth order
degenerate parabolic
PDE derived from a generalized model for
lubrication flows
of thin viscous fluid layers on solid
surfaces. There is a
critical mass for blow-up and a rich set of
dynamics
including families of similarity solutions
for finite-time
blow-up and infinite-time spreading. The
structure and
stability of the steady-states and the
compactly-supported
similarity solutions is studied.
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