In PDE of the type you show, especially when the PDE represents a physical phenomenon, terms like your N_lambda are referred to as the "flux." pdepe makes it easy to define boundary conditions where the flux equals a specified value, e.g. zero.
pdepe requires you to create a function to define your PDE. For your example it would look something like this:
function [c,f,s] = pdeDefinition(x,t,lam,dlamdx)
epsi=1;
Vm=2;
DLam=3;
nd=4;
ip=5;
F=6;
c = epsi/Vm;
f = DLam/Vm*dlamdx - nd*ip/F;
s = S+r;
end
The boundary condition function, which you also have to write, would look something like this.
function [pl,ql,pr,qr] = bcFunc(xl,lam_l,xr,lam_r,t)
pl = 0;
ql = 1;
pr = 0;
qr = 1;
end
