# System of Partial differential equations

I am trying to solve numerically a system of 3 partial differential equations and I am facing a problem.
My functions are f[x,t], g[x,t] and h[x,t] and are defined for x values between S and R (for some values of R and S).
The differential equations with the boundary conditions are 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]}; 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])};


With a bunch of 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;


Until there everything works and I can solve the system using the command

{fsol2, gsol2, hsol2} =  NDSolveValue[{eqnsNC, bc}, {f, g, h}, {x, S, R}, {t, 0, tf}]


However, for the real problem I need to add an additional constraint that states that the function f[x,t] is actually 0 on the region NN<x<R, for a value of NN such that S<NN<R and for all t. The boundary condition df/fx =0 in R is therefore redundant but I cannot implement the above constraint. I tried to change the boundary conditions by adding f[NN, t] == 0 but I am running into errors when trying to get the numerical solutions such as

NDSolveValue::bcedge: Boundary condition f[8,t]==0 is not specified on a single edge of the boundary of the computational domain. >>

How can I tell Mathematica to solve for f on the region S<x<R only and for h and g on the region R<x<S? Or is it possible to define a given set of equations on a particular domain (for example in my case for S<x<NN ) and another one for another region (NN<x<R)?

I would be very grateful for any advices you could think of !

Maud

• please post the equations using correct mathematica syntax. – george2079 Mar 10 '15 at 19:42
• To follow up on the comment by @george2079, edit your code so that it is in InputForm. For instance, \[PartialD]f(x,t)/\[PartialD]t should be D[f[x, t], t]. It also could be displayed as Derivative[0, 1][f][x, t]. – bbgodfrey Mar 11 '15 at 0:41
• And please also post the rest of the code. I.e There is an NDSolve message but no NDSolve command in your question. – user21 Mar 11 '15 at 8:04
• Hello, I am sorry for the wring syntax and I hope it is clearer now. Looking forward for your answers! – Maud Mar 16 '15 at 8:52