# Coupled differential equations

Posted 8 years ago
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 Hello, I am working on a system of three coupled differential equations describing the diffusion and complexation of a metal and a ligand. I am looking for the solution of the functions f[x,t], g[x,t] and h[x,t] on the region S < x < R. The system is the following: eqnsNC = { D[f[x, t],t]== DM * D[f[x, t], x,x]-kf * f[x, t] * h[x, t]+kdis * g[x, t], D[h[x, t], t]==DL * D[h[x, t], x,x]-kf * f[x, t] *h[x, t]+kdis * g[x, t],D[g[x, t], t]==DML * D[g[x, t], x,x]+kf * f[x, t] * h[x, t]-kdis *g[x, t]}; with the boundary conditions:  bc={f^(1,0)[R,t]==g^(1,0)[R,t]==h^(1,0)[R,t]==0, f[x,0]==g[x,0]==h[x,0]==0, f[S,t]==MS * (1-Exp[-1000 t]), g[S,t]==(kf * LS* MS * (1-Exp[-1000 t]))/kdis, h[S,t]==LS * (1-Exp[-1000 t])}; and some constants:  DM = 5*10^-6; DL = 5*10^-6; DML = 5*10^-6; kf = 10^3; kdis = 63.8; MS = 0.25; LS = 0.2; R = 0.12; NN = 0.1; S = 0.05; tf = 10000; I can then solve this system using the command: {fsol2, gsol2, hsol2} = NDSolveValue[{eqnsNC, bc}, {f, g, h}, {x, S, R}, {t, 0, tf}] The next step that is difficult for me is too add the extra condition that the function f[x,t] is identically 0 over the region NN <= x