# Classifying a diffusion equation

Diffusion in finite geometries Time-dependent diffusion in finite bodies can soften be solved using the separation of variables technique, which in cartesian coordinates leads to

## Classification of Symmetry Properties of the (1 + 2)

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## Diffusion equation

28 2. THE DIFFUSION EQUATION The corresponding basic solutions (2.2.4) to the heat equation are µi(x;t) = exp µ ¡ °i22 l2 t ¶ sin i l x; i = 1;2;3;:::: (2.2.12) By linear superposition of these

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## Group classification of systems of diffusion equations

Diffusion coefficient D =1 Initial distribution is: a) A stationary front: u(x,0)= (u−, for x ≤0, u+, for x >0. b) A stationary pulse: u(x,0)= u−, for x ∈[−L,−L/4], u+, for x ∈(−L/4,L/4), u−, for x ∈[L/4,L].

## Symmetry classification of time-fractional diffusion equation

Diffusion is the process of movement of molecules under a concentration gradient. It is an important process occurring in all living beings.

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