how can i solve two coupled PDEs simultaneously?

well i have this problem that i want to solve the diffusion equation, dH/dt' = d/dx(D * dH/dx), and i know such a question had been asked but it's still not answered in the answers. in my case i want to solve this equation but not only my diffusion coefficient is not constant but is dependent on m (as reactive sites concentration) but this concentration is defined through another PDE as: dm/dt=kmH so these two equations should be solve simultaniously and i know best way is to solve them by difference method but i don't know how to do the coding and implement m inside H and vice versa. can anyone show me an example of how to do such a thing? thanks alot.