Derive a diffusion equation on the basis of the physical law $q=−D(n−n_0)^2n^2\frac{∂n}{∂x}+nv$

Question

It is given that the mass flux density q of a substance in medium obeys the following physical law:

$$q=−D(n−n_0)^2n^2\frac{∂n}{∂x}+nv$$ where $n(x,t)$ is the concentration $([n]=ML−3)$ of the substance in the medium as a function of the space coordinate $x$ and time $t$, $D$ is a constant coefficient of diffusion, $n_0$ is a constant parameter of the problem and $v(x,t)$ is macroscopic velocity of the medium.

Derive a diffusion equation on the basis of the physical law.

Ive worked out that $D=M^{-5}L^{16}T$ but I'm really not confident with diffusion equations so any help towards the answer will be appreciated.

Answer 1

Dump this into the continuity equation, $$\frac{\partial n}{\partial t}+\frac{\partial q}{\partial x}=0.$$ The PDE follows from calculating the derivatives.