14. This problem studies the steady state system related to a reaction-diffusion system modeling a flocculation process in an un-stirred chemostat, where the isolated or planktonic bacteria naturally aggregate reversible to one another to form macroscopic flocs. Specifically, we are interested in solutions to the system -doSxx + Sx =-f(S)u- g(5)v. Osx51, -djurx + u, = f(S)u+ B(u.v.)v--a(u.v)u. 0sxs1, yu -davis + v, = g(S)v + a(u, v)u - -B(u.v)v, Osxs1, yu -doS, (0) + 5(0) = 1. 5,(1) = 0, -dju, (0) + u(0) = 0, u, (1) = 0, -divx(0) + v(0) = 0, v.(1) = 0. Here, a (u, v) = (u + v)v, B(u, v) = (1 + v)(u + v), j = > = 10"), do = 1, dj = 1, dz = 10. f (S) = = and g(S) = S(x) is the substrate concentration, and u(x) and v(x) denote the concentrations of isolated and attached bacteria. f and g represent the per-capita growth rates of the isolated and attached bacteria, a and 8 denote the component wise flocculation and deflocculation rates. Solutions to this system are only physically relevant if 0 s S(x) $ 1, u(x) 2 0 and v(x) 2 0. a. Show that the constant functions S(x) = 1, u(x) = v(x) = 0 for 0 s x $ 1 are solutions to this system. b. Determine whether there are other physically relevant solutions, and if so, describe your process for finding them, and graph them