Diffusion equation
Assuming that the flux is proportional to the gradient
∇u but pointing in the opposite direction
since the flow is from regions of high concetration to lower concentrations, we obtain
ρ=−D∇u,
resulting in
div∇u=DΔu=0,
which is Laplace's equation. The constant
D can be coupled with various physical
constants, such as the diffusion constant or the specific heat and thermal conductivity discussed below.