
driftdiffusion equation
I have the next driftdiffusion equation:
$\displaystyle \frac{\partial \phi(x,y,z)}{\partial t} + u_x(z) \frac{\partial \phi(x,y,z)}{\partial x} = \nabla D(z) \nabla \phi (x,y,z)$
where D(z) is a matrice.
To solve this equation i perform the next change of variable: $\displaystyle X = x + u(z) t , Y= y , Z=z, T=t$ 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 or taking into account in the change of variable $\displaystyle \nabla D(z)$ like for example $\displaystyle Z=z  \nabla D(z)$ or maybe I should replace also in $\displaystyle \nabla D(z)$ the change of variable (I replace only in $\displaystyle \phi$). I am not sure if I can doing this options. Some one can help me?