Asymptotics for the spectrum of a thin film equation in a singular limit


Kitavtsev G., Recke L., Wagner B.

SIAM Journal on Applied Dynamical Systems, cilt.11, sa.4, ss.1425-1457, 2012 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 4
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1137/100813488
  • Dergi Adı: SIAM Journal on Applied Dynamical Systems
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1425-1457
  • Orta Doğu Teknik Üniversitesi Kuzey Kıbrıs Kampüsü Adresli: Hayır

Özet

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.