Self-adjoint sub-classes of generalized thin film equations

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): MS Bruzon, ML Gandarias, Nail H. Ibragimov
Title: Self-adjoint sub-classes of generalized thin film equations
Journal: Journal of Mathematical Analysis and Applications
Year: 2009
Volume: 357
Issue: 1
Pagination: 307-313
ISSN: 0022-247X
Publisher: Academic Press
URI/DOI: 10.1016/j.jmaa.2009.04.028
ISI number: 000266507400030
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
Language: English
Abstract: In this work we consider a class of fourth-order nonlinear partial differential equation containing several tin-specified coefficient functions of the dependent variable which encapsulates various mathematical models used, e.g. for describing the dynamics of thin liquid films. We determine the subclasses of these equations which are self-adjoint. By using a general theorem on conservation laws proved by one of the authors (NHI) we find conservation laws for some of these partial differential equations without Classical Lagrangians.
Subject: Mathematics\General
Keywords: Adjoint equation to nonlinear equations; Lagrangian; Symmetry of adjoint equations; Conservation laws; Thin film equations