Symmetry properties for a generalised thin film equation

Symmetry properties are presented for a fourth-order parabolic equation written in conservation form. It was introduced in the literature as a generalisation of the fourth-order thin film equation. We derive equivalence transformations, Lie symmetries, potential symmetries, non-classical symmetries...

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Bibliographic Details
Published in:Journal of engineering mathematics 2013-10, Vol.82 (1), p.109-124
Main Authors: Charalambous, Kyriakos, Sophocleous, Christodoulos
Format: Article
Language:English
Subjects:
Applications of Mathematics
Chains
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Theoretical and Applied Mechanics
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Summary:Symmetry properties are presented for a fourth-order parabolic equation written in conservation form. It was introduced in the literature as a generalisation of the fourth-order thin film equation. We derive equivalence transformations, Lie symmetries, potential symmetries, non-classical symmetries and potential non-classical symmetries. A chain of such equations is introduced. We conclude by presenting similar results for the third-order equation of this chain.
ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-012-9577-6