Problem solving coupled PDEs with NDSolve

Questions
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1

I have the following system of PDEs for which I have given parameters \gamma, \tau and \mu,

\begin{align} T_t = &\ \gamma\,(L +\tau F-T)\\ F_t = & -F_x-(F-LT)\\ L_t = &\ \mu L_{xx}+(F-LT)\end{align}

with no flux boundary conditions at x=0 and x=\infty for F and L. The initial conditions are L=T=F=e^{-x^2}. I tried to find a travelling wave solution to this problem, and I encountered an error while trying to set boundary conditions for F as the order of the derivative in the boundary condition was equal to that in the given system. To solve that, I proceeded in accordance to:

http://mathematica.stackexchange.com/questions/72489/too-high-differential-order-in-boundary-conditions

but encountered further issues. This is my code:

gam = 1;
tau = 0.6;
mu = 0.2;
n = 100;
time = 10;

sys = {Derivative[0, 1][T][x, t] == 
         gam*(L[x, t] + tau*F[x, t] - T[x, t]),
       Derivative[1, 1][F][x,t] == 
         -Derivative[2, 0][F][x, t] - Derivative[1, 0][F][x, t] - 
           D[L[x, t]*T[x, t], x]),
       Derivative[0, 1][L][x, t] == 
         mu*Derivative[2, 0][L][x, t] + (F[x, t] - L[x, t]*T[x, t]),
       L[x, 0] == Exp[-x^2],
       T[x, 0] == Exp[-x^2],
       F[x, 0] == Exp[-x^2],
       Derivative[1, 0][F][0, t] == 0,
       Derivative[1, 0][F][n, t] == 0,
       Derivative[1, 0][L][0, t] == 0,
       Derivative[1, 0][L][n, t] == 0,
       Derivative[0, 1][F][0,0] == 
         -Derivative[1, 0][F][0, 0] - (F[0, 0] - L[0, 0]*T[0, 0])
   };
sol = NDSolve[sys, {T, F, L}, {x, 0, n}, {t, 0, time}];

I am getting the following error message:

NDSolve::bcedge: Boundary condition (F^(0, 1))[0, 0] == -F[0, 0] + L[0, 0] T[0, 0] - (F^(1, 0))[0, 0] is not specified on a single edge of the boundary of the computational domain. >>

Any help is appreciated!

2

F has only a fist order derivative in x how can it have 2 boundary conditions (at x=0 and at x->infinity)