Continuous and Discrete Transformations of a One-Dimensional Porous Medium Equation

DOI

10.2991/jnmp.1999.6.4.1How to use a DOI?

Abstract

We consider the one-dimensional porous medium equation ut = (un ux)x + µ x un ux. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction of a new dependent variable this partial differential equation can be equivalently written as a system of two equations. Point transformations are also sought for this auxiliary system. It turns out that in addition to the continuous point transformations that may be derived by Lie's method, a number of discrete transformations are obtained. In some cases the point transformations which are presented here for the single equation and for the auxiliary system form cyclic groups of finite order.

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/).

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TY  - JOUR
AU  - Christodoulos Sophocleous
PY  - 1999
DA  - 1999/11/01
TI  - Continuous and Discrete Transformations of a One-Dimensional Porous Medium Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 355
EP  - 364
VL  - 6
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.4.1
DO  - 10.2991/jnmp.1999.6.4.1
ID  - Sophocleous1999
ER  -