{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T15:26:24Z","timestamp":1787239584388,"version":"build-2736575974"},"reference-count":28,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>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 $\\varepsilon$ 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 $\\varepsilon\\to0$. 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 $\\varepsilon$.<\/jats:p>","DOI":"10.1137\/100813488","type":"journal-article","created":{"date-parts":[[2012,10,25]],"date-time":"2012-10-25T12:37:13Z","timestamp":1351168633000},"page":"1425-1457","source":"Crossref","is-referenced-by-count":7,"title":["Asymptotics for the Spectrum of a Thin Film Equation in a Singular Limit"],"prefix":"10.1137","volume":"11","author":[{"given":"Georgy","family":"Kitavtsev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lutz","family":"Recke","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Barbara","family":"Wagner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,10,25]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.67.016302"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0001-8686(01)00055-0"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.69.931"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.81.1131"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/14\/6\/309"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.64.031602"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.021601"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2005.06.010"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1063\/1.1758911"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792508007559"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/080713732"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1007\/s10665-009-9313-z"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(91)90163-4"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9590.00149"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.54.4568"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/050630192"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.016301"},{"issue":"925","key":"atypb18","first-page":"1","volume":"198","author":"Mielke A.","year":"2009","journal-title":"Mem. Amer. Math. Soc."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/24\/8\/010"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/PL00004234"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1063\/1.869795"},{"key":"atypb22","unstructured":"G. Kitavtsev,\n                      Derivation, Analysis and Numerics of Reduced ODE Models Describing Coarsening Dynamics of Liquid Droplets\n                      , Ph.D. thesis, Institute of Mathematics, Humboldt University of Berlin, Berlin, Germany, 2009; available online from https:\/\/www.svh-verlag.de\/catalog\/details\/store\/gb\/ book\/978-3-8381-2328-8\/reduced-ode-models-describing-coarsening-dynamics-of-liquid-droplets."},{"key":"atypb23","unstructured":"J. Kevorkian and J. D. Cole,\n                      Perturbational Methods in Applied Mathematics\n                      , Appl. Math. Sci. 34, Springer-Verlag, Berlin, Heidelberg, New York, 1981."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895281484"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500005060"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.01.017"},{"key":"atypb27","first-page":"189","author":"O'Malley R. E.","year":"1996","journal-title":"Philadelphia"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/1017005"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/100813488","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:40:32Z","timestamp":1787236832000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/100813488"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1137\/100813488"],"URL":"https:\/\/doi.org\/10.1137\/100813488","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1]]}}}