For (5) we have the following:
Set
V is the space of functions for both u and v since Dirichlet boundary condition is zero.
Multiply 
by 
. Integrating by parts, we get :
Variational Formulation is
For (7) we have the following:
Variational Formulation is
Variational formulations for (6) and (8) have a
term on the right hand side.