Probably this is a trivial question.
I am trying to find stationary solutions (steady state solution) of $$ \frac{\partial u}{\partial t} = \nabla. (f(x) u) - D \nabla^2 u $$ where $f(x)$ is a vector valued function and D is a positive scaler.
So I want to solve: $$ \nabla. (f(x) u) = D \nabla^2 u $$ I will be thankful if you can point to out to references that deals with sort of problems.