Hoe to define geometry and Neuman BCs in system of PDEs

I'm trying to solve a system of three non-linear coupled PDEs using Partial Differential Equation Toolbox. The three functions are only function of t and x, and I want to solve this in the domain: t between 0 and tmax, x between 0 and L.

1. How should I define the geometry in this case? Is it going to be a rectangle in which one axis is t and the other x?

Also, for example, for one of the functions, the BCs are: u1'(0,t)=u1(0,t)/c1 and u1'(L,t)=c2/func(L,t) where c1, c2 are constants and func is a function of t and x. These are Neuman BCs, so the second question is:

2. How should I implement these BC's using applyBoundaryCondition?