Question about Variational Formulation

i have two questions please

Q_T = [0,L] x [0,H] x [0,T]

1- We have the following variational formulation:

\int_{Q_T} dV/dt \psi dx dy dt = - D \int_{Q_T} \nabla V . \nabla \psi dx dy dt + D \int_0^T \int_0^L \psi(x,0,t) (\gamma VC - h Vf) dx dt - u0 \int_{Q_T} y \dV/dx \psi dx dy dt - \sigma_2 \int_{Q_T} V \psi dx dy dt

is it’s following formulation with FF++ is correct

problem system2(V,VH,solver=UMFPACK)=

​2- what is the mathematical problem corresponding to the FF++ formulation:

problem extend(Vk,Vt) = int2d(Th)(dy(Vk)*dy(Vt)) + on(1,Vk=V);


I add that

mesh Th = square(N,N,[L*x,H*y]);

fespace Vh(Th,P1);