Next Article in Journal
A Prototype of Speech Interface Based on the Google Cloud Platform to Access a Semantic Website
Previous Article in Journal
Cryptanalysis of an Image Encryption Algorithm Based on Combined Chaos for a BAN System, and Improved Scheme Using SHA-512 and Hyperchaos
Previous Article in Special Issue
Some Approaches to the Calculation of Conservation Laws for a Telegraph System and Their Comparisons
Article Menu

Export Article

Open AccessArticle
Symmetry 2018, 10(7), 267; https://doi.org/10.3390/sym10070267

Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity

1,* and 2
1
Department of Information and Computational Science, He’nan Agricultural University, Zhengzhou 450002, China
2
Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
*
Author to whom correspondence should be addressed.
Received: 23 April 2018 / Revised: 1 July 2018 / Accepted: 2 July 2018 / Published: 7 July 2018
View Full-Text   |   Download PDF [300 KB, uploaded 7 July 2018]

Abstract

The radially symmetric nonlinear reaction–diffusion equation with gradient-dependent diffusivity is investigated. We obtain conditions under which the equations admit second-order conditional Lie–Bäcklund symmetries and first-order Hamilton–Jacobi sign-invariants which preserve both signs (≥0 and ≤0) on the solution manifold. The corresponding reductions of the resulting equations are established due to the compatibility of the invariant surface conditions and the governing equations. View Full-Text
Keywords: conditional Lie–Bäcklund symmetry; differential constraint; sign-invariant; nonlinear reaction–diffusion equation; symmetry reduction conditional Lie–Bäcklund symmetry; differential constraint; sign-invariant; nonlinear reaction–diffusion equation; symmetry reduction
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

Ji, L.; Feng, W. Second-Order Conditional Lie–Bäcklund Symmetries and Differential Constraints of Nonlinear Reaction–Diffusion Equations with Gradient-Dependent Diffusivity. Symmetry 2018, 10, 267.

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