Spectrum asymptotics for the linearized thin film equation

• Published in: Proceedings in applied mathematics and mechanics Vol. 8; no. 1; pp. 10727 - 10728
• Main Authors: Kitavtsev, G., Recke, L., Wagner, B.
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag 01.12.2008; WILEY‐VCH Verlag
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.200810727

In this paper we describe linear stability properties for the special type of thin film equation corresponding to a presence both destabilizing van der Waals and stabilizing Born forces in the intermolecular interactions. The final stage of the evolution described by such type equation is characterized by the slow–time coarsening dynamics after formation of an array of droplets. Finally the dynamics converges to one stationary droplet. We derive analytically the asymptotics for the spectrum of the thin film equation linearized at one droplet steady state with respect to small parameter ϵ (describing the form of droplet) tending to zero. This asymptotics is confirmed by numerical investigations as well. The analytical approach can be applied also for the investigation for the spectrum of the thin film equation linearized at an array of droplets. Our results considerably extend the ones derived in [4]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)