Symmetries and Invariant Solutions for the Thermal Expulsion Equation


Maha Falih Jassim

Commission of Technical Education, Technical Institute\ Kirkuk, Kurdistan Region Iraq





Abstract
In this paper we study the classical Lie symmetries method for a two dimensional partial differential
equation (PDE) which is called the Thermal Expulsion Equation, and we obtained reductions to an ordinary
differential equation of a second order (ODE) called principal (ODE).Then we analyzed some problems of
the Thermal Expulsion Equation when it is invariant to the stretching group to derive an approximate
solution of the Expulsion equation corresponding to impulsive boundary conditions, when these conditions
are clamped and a slowly varying happens in them with respect to time again.

Keyword: Lie symmetries, classical symmetries, similarity solutions, and invariant solutions



References

1- Turk.C, Discrete Symrnetries of Nonlinear Ordinary Differential Equations, Luleal University of Technology, 2003.
2- Hydon .P.H, Symmetry Methods for Dffirential Equation,Cambridge Press,2001'
3- Michor, P.W., Lie Theory and Applications,From Internet, 2002'
4- Cantwfll,B.J., Intraduction onti Symmetry Analysis,Cambridge university press, 20t2, t21-275
5- Parmar, A., Applying Lie Group Symmetry to Solving Dffirential Equation University of New
6- Avramidi,l.,Notes on Lie Group, From Intemet,200l.
7- Burde, G., Expanded Lie Cioup Transformations and Similarity Reductions of
Differential Equations, Journal of institute of Mathematics of NAS of Ukraine,2002, 43pari l ,93-1001. 
8- Dresner, L., Application of Lie's Theory of Ordinary and Partial Dffirential Equations, IOP, Publishing Ltd, 1999.
9- F;rdy, A,P., Lie Group, Lie Algebra and Symmetry of Dffirential Equation, University of Leeds,2003.
10-] Gungrr,F., Sy*rnetries snd Invariant Solution of Two - Dimensional Variable
to ffiiient Burger Equation,J.Phys,A:Math, 2001, (34) , ,4313-4321'
11- Ivlaharana, K., On Lie Point Symmetry of Classical Wess'Zumina Modle, Hep-  th/oi06198,2001 (1).
12- Karasu, A., On' the Lie Symmetries of Kepler-Ermakov Systems, Journal of
Nonlinear Mathematies Physics 2002, 9, 4, 47 5 -482.
13- Zheng, L., Similarity Solution to a Heat Equation in an Infinite Medium, Journal of
University of science and Technology Beijing,2003, 10, 4'
14- pakdemirli M., Comparison of Lpproximate symmetry Methods for Differential
Equations Journal of Acta Applicandae Matheticae 20A4 L29'
l5-Tsyfra, I., on the Symmetry Approach to Reduction of Patrial Differential Equation,
Journal of Math -ph, 2004 ,1.