Math @ Duke

Publications [#244240] of Thomas P. Witelski
search www.ams.org.Papers Published
 Bowen, M; Witelski, TP, The linear limit of the dipole problem for the thin film equation,
SIAM Journal on Applied Mathematics, vol. 66 no. 5
(2006),
pp. 17271748, ISSN 00361399 [050637832], [doi]
(last updated on 2017/12/17)
Abstract: We investigate selfsimilar solutions of the dipole problem for the onedimensional thin film equation on the halfline {x ≥ 0}. We study compactly supported solutions of the linear moving boundary problem and show how they relate to solutions of the nonlinear problem. The similarity solutions are generally of the second kind, given by the solution of a nonlinear eigenvalue problem, although there are some notable cases where firstkind solutions also arise. We examine the conserved quantities connected to these firstkind solutions. Difficulties associated with the lack of a maximum principle and the nonselfadjointness of the fundamental linear problem are also considered. Seeking similarity solutions that include sign changes yields a surprisingly rich set of (coexisting) stable solutions for the intermediate asymptotics of this problem. Our results include analysis of limiting cases and comparisons with numerical computations. © 2006 Society for Industrial and Applied Mathematics.


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