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SIAM Journal on Applied Dynamical Systems, vol.11, no.4, pp.1425-1457, 2012 (SCI-Expanded)
In this paper the linear stability properties of the steady states of a no-slip lubrication equation are studied. In the physical context, these steady states correspond to configurations of droplets that arise during the late-phase dewetting process under the influence of both destabilizing van der Waals and stabilizing Born intermolecular forces, which in turn give rise to the minimum thickness e of the remaining film connecting the droplets. The goal of this paper is to give an asymptotic description of the eigenvalues and eigenfunctions of the problem, linearized about the one-droplet solutions, as ε → 0. For this purpose, corresponding asymptotic eigenvalue problems with piecewise constant coefficients are constructed such that their eigenvalue asymptotics can be determined analytically. A comparison with numerically computed eigenvalues and eigenfunctions shows good agreement with the asymptotic results and the existence of a spectrum gap for sufficiently small ε. © 2012 Society for Industrial and Applied Mathematics.