I have a question regarding an equation for changes in chemical concentration. The chemical concentration we are looking at changes due to diffusion, decay and production of the chemical. Since the diffusion happens so much faster than the other two, it is given that we can you a so-called quasi-steady assumption. This then gives the equation:
$$D \nabla^2c-a \cdot c+b\cdot c=0$$
where $a$ and $b$ are rates of decay and production, respectively. $c$ is the chemical concentration and D is the diffusion coefficient.
Is it correct that the reason we only have a derivative expression for the diffusion because it happens so fast relative to the other two, and therefore we can assume the chemical concentration for the two other processes to remain constant (using the quasi steady assumption), or is that not a correct reasoning for why the equation has the simple expression for decay and production, while we need a more complex expression for diffusion?