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

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