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 germanaries November 15th, 2007 01:53 PM

drift-diffusion equation

I have the next drift-diffusion equation:

\frac{\partial \phi(x,y,z)}{\partial t} + u_x(z) \frac{\partial \phi(x,y,z)}{\partial x} = \nabla D(z) \nabla \phi (x,y,z)

where D(z) is a matrice.
To solve this equation i perform the next change of variable:
X = x + u(z) t , Y= y , Z=z, T=t
and then I apply the Fourier transformation and when I solve this integrals with maple, at the first integral maple said that it is undefined.

Maybe I can solve the problem applying other change of variable taking into account for example
Z=z - \nabla D(z)
or maybe I should replace also in
\nabla D(z)
the change of variable. I am not sure if I can doing this options. Could someone help me?

p.s. I cannot write in LaTex, I don´t know why.

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