Conservation laws and Lie symmetries a (2+1)-dimensional thin film equation

This paper considers a generalized thin film equation in two spatial dimensions depending on three arbitrary functions. This equation describes the time evolution of a Newtonian liquid that is considerably thinner in one direction than in the other directions. We include a classification of point sy...

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Bibliographic Details
Published in:Journal of mathematical chemistry 2019-05, Vol.57 (5), p.1243-1251
Main Authors: Recio, Elena, Garrido, Tamara M., de la Rosa, Rafael, Bruzón, María S.
Format: Article
Language:English
Subjects:
Chemistry
Chemistry and Materials Science
Conservation laws
Math. Applications in Chemistry
Newtonian liquids
Original Paper
Physical Chemistry
Theoretical and Computational Chemistry
Thin films
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Summary:This paper considers a generalized thin film equation in two spatial dimensions depending on three arbitrary functions. This equation describes the time evolution of a Newtonian liquid that is considerably thinner in one direction than in the other directions. We include a classification of point symmetries and the corresponding transformation groups. We derive all low-order local conservation laws of the equation in terms of the arbitrary functions. In addition, we discuss the physical meaning of the conserved quantities and provide a useful conservation identity.
ISSN:0259-9791
1572-8897
DOI:10.1007/s10910-018-0945-y