This models solves the problem represented by the following PDE by means of the finite volume method, on a spatial domain of unit length and assuming unit velocity v.
If μ = 0, the model represent the transport of a certain chemical species in a fluid, similar to SimpleAdvection. If mu is increased, a chemical reaction is added with two stable equilibria, one at u = 0 and one at u = 1, with an unstable equilibrium at u = α.
The chemical reaction sharpens the concentration wave front, which would be otherwise be smoothed out by the numerical diffusion effect of the finite volume method.
The boundary condition u_in at the inlet, i.e., u(0,t), is specified by suitable binding equations.