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| Publications [#10221] of Thomas P. Witelski
search www.ams.org.Papers Published
- A. J. Bernoff and Thomas P. Witelski, Linear stability of source-type similarity solutions of the thin film equation,
Applied Mathematics Letters 18 (2002) pp. 599--606.
(last updated on 2002/08/21)
Abstract:
We study the stability of compactly-supported source-type
self-similar solutions of the generalized lubrication
equation
$h_t=-(h^nh_{xxx})_x$.
Using linear stability analysis, applied to the problem in
similarity
variables, we show that the source-type solutions are
stable. These results
are related to the underlying symmetries of the PDE. For the
special
case of $n=1$, analytical results are obtained for the
spectrum, and the
eigenfunctions are given in terms of classical orthogonal
polynomials.
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