Journal of Physical Mathematics
- J. Phys. Math.
- Volume 2 (2010), Article ID P100508, 19 pages.
Lie symmetries and exact solutions of a class of thin film equations
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.
J. Phys. Math., Volume 2 (2010), Article ID P100508, 19 pages.
First available in Project Euclid: 25 October 2010
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Zentralblatt MATH identifier
Primary: 35K50 35K60: Nonlinear initial value problems for linear parabolic equations
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