Density-limited diffusion

Hi,

I'm trying to solve a set of 3 PDEs where one of the diffusion in one of the PDEs is limited by the value of one of the other variables, something like this:
ut=...
vt=vx*(D*(1-u))+...
when I run it but it reaches singularity.
Does anyone has an idea of how to solve it or had this problem before?

Thanks,
Tamir.