Volume 6, Issue 4, November 1995, Pages 355 - 364
Continuous and Discrete Transformations of a One-Dimensional Porous Medium Equation
Available Online 1 November 1995.
- https://doi.org/10.2991/jnmp.19184.108.40.206How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - Christodoulos SOPHOCLEOUS PY - 1995 DA - 1995/11 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.19220.127.116.11 DO - https://doi.org/10.2991/jnmp.1918.104.22.168 ID - SOPHOCLEOUS1995 ER -