Journal of Nonlinear Mathematical Physics

Volume 3, Issue 1-2, May 1996, Pages 130 - 138

Perturbed Lie Symmetry and Systems of Non-Linear Diffusion Equations

Authors
R.J. WILTSHIRE
Corresponding Author
R.J. WILTSHIRE
Available Online 19 December 2006.
DOI
https://doi.org/10.2991/jnmp.1996.3.1-2.14How to use a DOI?
Abstract
The method of one parameter, point symmetric, approximate Lie group invariants is applied to the problem of determining solutions of systems of pure one-dimensional, diffusion equations. The equations are taken to be non-linear in the dependent variables but otherwise homogeneous. Moreover, the matrix of diffusion coefficients is taken to differ from a constant matrix by a linear perturbation with respect to an infinitesimal parameter. The conditions for approximate Lie invariance are developed and are applied to the coupled system. The corresponding prolongation operator is derived and it is shown that this places a power law and logarithmic constraints on the nature of the perturbed diffusion matrix. The method is used to derive an approximate solution of the perturbed diffusion equation corresponding to impulsive boundary conditions.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
3 - 1
Pages
130 - 138
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1996.3.1-2.14How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - R.J. WILTSHIRE
PY  - 2006
DA  - 2006/12
TI  - Perturbed Lie Symmetry and Systems of Non-Linear Diffusion Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 130
EP  - 138
VL  - 3
IS  - 1-2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.1-2.14
DO  - https://doi.org/10.2991/jnmp.1996.3.1-2.14
ID  - WILTSHIRE2006
ER  -