The diffusion equaiton is a
Partial Differential Equation.
If a function N is dependant on two
variables N(x,y) say, then
the diffusion equation equates the second
derivitave
in one
variable to the first derivative in the other
variable.
a N_xx = b N_y
where a and b are constants. This equation
describes heat flow with y being identifies with time
and x being identified with space.