Coupled reaction diffusion equations

I am still quite newbie and I am trying to implement a reaction diffusion model which writes:

\partial_t u=D_u\nabla^2 u +u-u^3-v+k
\tau\partial_t v=D_v\nabla^2 v +u-v

where I have to unknowns : u and v. I roughly know how to write a weak formulation for the diffusion of a single species, but I am quite lost on how to proceed for two species, with coupled PDE and how to implement that in freefem. Would anyone have recommendations on that topic ?

Have a great day,



See one of the examples for Navier-Stokes. Remove continuity/pressure and change the terms to match what is shown in your equations.

Hi Chris,

Thanks a lot for your indication - I am going to see what I can make out of it, based on my rather low level in math and freefem :wink: - don’t ask me why I have to teach something I don’t understand well myself…