Next Article in Journal
Accountability Requirements in the Cloud Provider Chain
Next Article in Special Issue
Lie Symmetries of Nonlinear Parabolic-Elliptic Systems and Their Application to a Tumour Growth Model
Previous Article in Journal
Cosmetic Detection Framework for Face and Iris Biometrics
Previous Article in Special Issue
Nonclassical Symmetries of a Power Law Harry Dym Equation
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessFeature PaperReview
Symmetry 2018, 10(4), 123; https://doi.org/10.3390/sym10040123

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

1,†,* , 2,†
and
2,†
1
Institute of Mathematics, National Academy of Science of Ukraine, 3, Tereshchenkivs‘ka Street, 01004 Kyiv, Ukraine
2
Department of Mathematics, Poltava National Technical Yuri Kondratyuk University, 24, Pershotravnevyi Prospekt, 36011 Poltava, Ukraine
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 13 March 2018 / Revised: 11 April 2018 / Accepted: 12 April 2018 / Published: 20 April 2018
View Full-Text   |   Download PDF [4833 KB, uploaded 3 May 2018]   |  

Abstract

This review is devoted to search for Lie and Q-conditional (nonclassical) symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented. View Full-Text
Keywords: reaction-diffusion-convection equation; exponential nonlinearity; Lie symmetry; Q-conditional (nonclassical) symmetry; exact solution reaction-diffusion-convection equation; exponential nonlinearity; Lie symmetry; Q-conditional (nonclassical) symmetry; exact solution
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Cherniha, R.; Serov, M.; Pliukhin, O. Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions. Symmetry 2018, 10, 123.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top