This is a system of PDEs in two dependent variables \(u\) og \(v\), both functions of one time variable \(t\) and any number of spatial variables \(x_i\). The general form is \[u_t = r_u\nabla^2 u -u v^2+f(1-u)\] \[v_t = r_v\nabla^2 v + uv^2-(f+k)v \]

You should find appropriate values for \(r_u\), \(r_v\) and the parameters \(f\) and \(k\). In light of the intended application, what are appropriate initial values/boundary conditions? The system is most interesting where there are 2 spatial dimensions, but it will suffice to study just one.

Google: Gray-Scott equations, diffusion-reaction equation, chemical reactions.

Challenges: 2 space dimensions, application.