System of two equations

i have to resolve two following equations in 2D domain : [0,L] x[0,H]
dV/dt = D* Delta V - dV/dx - V
dU/dt= V(x,0,t) - U (where V is the solution of the first equation).
with boundary conditions
x=0,L: dV/dx = 0, y=0: dV/dy=- U + V(x,0,t); y=H: dV/dy=0
avec initial condition V(x,y,0)= V0

My questions are:
1-how we can exprime V(x,0,t) in the variational formulation of second equation to resolve the system?
2- How we can define the boundary conditions of V with FF++?