Perturbed Lie Symmetry and Systems of Non-Linear Diffusion Equations

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - R.J. Wiltshire
PY  - 1996
DA  - 1996/05/01
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  - 10.2991/jnmp.1996.3.1-2.14
ID  - Wiltshire1996
ER  -