Moving boundary problems and non-uniqueness for the thin film equation

Authors
King, JR Bowen, M
Citation
Jr. King et M. Bowen, Moving boundary problems and non-uniqueness for the thin film equation, EUR J AP MA, 12, 2001, pp. 321-356
Citations number
20
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
ISSN journal
09567925 → ACNP
Volume
12
Year of publication
2001
Part
3
Pages
321 - 356
Database
ISI
SICI code
0956-7925(200106)12:<321:MBPANF>2.0.ZU;2-Z
Abstract
A variety of mass preserving moving boundary problems for the thin film equ ation, u(t) = -(u(n)u(xxx))(x), are derived (by formal asymptotics) from a number of regularisations, the case in which the substrate is covered by a very thin pre-wetting film being discussed in most detail. Some of the prop erties of the solutions selected in this fashion are described, and the ful l range of possible mass preserving non-negative solutions is outlined.