Here is something I threw together, it is definitely incorrect, as the program is throwing errors. In particular, a
SolutionVariableNumberError is raised. Likely this is because the equations are written incorrectly. The likely suspect, I'm guessing is in the
SourceTerm's. This is a start though for how one might go about solving these equations in FiPy.
Perhaps someone in the forum has more experience with this tool and can elaborate on what is going wrong here. Other than that if you want to continue with this tool, I suggest reading and studying more of FiPy's examples. You could also post to the their mailing list, and ask for some help writing the equations. I've seen others do this on the list, as I have been following it for a while. The project maintainers are quite helpful. (I have no affiliation to the project, I'm just a fan).
from fipy import CellVariable
from fipy import DiffusionTerm
from fipy import Grid1D
from fipy import ImplicitSourceTerm
from fipy import numerix
from fipy import PowerLawConvectionTerm
from fipy import TransientTerm
mu = 1.
gam = 1.
tau = 1.
m = Grid1D(nx=100,Lx=1.)
L = CellVariable(mesh=m, hasOld=True)
F = CellVariable(mesh=m, hasOld=True)
T = CellVariable(mesh=m, hasOld=True)
x = m.cellCenters
L.value = numerix.exp(-x**2)
F.value = numerix.exp(-x**2)
T.value = numerix.exp(-x**2)
eqn0 = TransientTerm(var=L) == DiffusionTerm(mu, var=L) + (ImplicitSourceTerm(var=F) - ImplicitSourceTerm(var=L*T))
eqn1 = TransientTerm(var=F) == PowerLawConvectionTerm(-1., F) - (ImplicitSourceTerm(var=F) - ImplicitSourceTerm(var=L*T))
eqn2 = TransientTerm(var=T) == gam * (ImplicitSourceTerm(1., var=L) + ImplicitSourceTerm(tau, var=F) + ImplicitSourceTerm(-1.,var=T))
eqn = eqn0 & eqn1 & eqn2
for t in range(100):