Journal of Physical Mathematics

Lie symmetries and exact solutions of a class of thin film equations

Roman Cherniha and Liliia Myroniuk

Full-text: Open access

Abstract

A symmetry group classification for fourth-order reaction-diffusion equations, allowing for both second-order and fourth-order diffusion terms, is carried out. The fourth-order equations are treated, firstly, as systems of second-order equations that bear some resemblance to systems of coupled reaction-diffusion equations with cross diffusion, secondly, as systems of a second-order equation and two first-order equations. The paper generalizes the results of Lie symmetry analysis derived earlier for particular cases of these equations. Various exact solutions are constructed using Lie symmetry reductions of the reaction-diffusion systems to ordinary differential equations. The solutions include some unusual structures as well as the familiar types that regularly occur in symmetry reductions, namely, self-similar solutions, decelerating and decaying traveling waves, and steady states.

Article information

Source
J. Phys. Math., Volume 2 (2010), Article ID P100508, 19 pages.

Dates
First available in Project Euclid: 25 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.jpm/1288015976

Digital Object Identifier
doi:10.4303/jpm/P100508

Zentralblatt MATH identifier
1264.74156

Subjects
Primary: 35K50 35K60: Nonlinear initial value problems for linear parabolic equations

Keywords
Lie symmetries exact solutions thin film equations

Citation

Cherniha, Roman; Myroniuk, Liliia. Lie symmetries and exact solutions of a class of thin film equations. J. Phys. Math. 2 (2010), Article ID P100508, 19 pages. doi:10.4303/jpm/P100508. https://projecteuclid.org/euclid.jpm/1288015976


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