Please use this identifier to cite or link to this item: https://evnuir.vnu.edu.ua/handle/123456789/17756
Title: Lie symmetries and exact solutions of a class of thin film equations
Authors: Cherniha, Roman
Myroniuk, Liliia
Bibliographic description (Ukraine): Cherniha R. Myroniuk L. Journal of Physical Mathematics. Vol. 2 (2010) . 19 p.
Issue Date: 2010
Date of entry: 2-Jun-2020
Keywords: Lie symmetries
Exact solutions
thin film equations
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.
URI: http://evnuir.vnu.edu.ua/handle/123456789/17756
Content type: Article
Appears in Collections:Наукові роботи (FITM)

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