1D equation in 2D simulation
 

Dear All,

I am wondering if it's possible to include a solution of a 1D equation in a higher dimensional simulation. Symbolically the problem I am trying to solve is this:

F( \theta(x,y) ) = \lambda(x)
G(\lambda(x)) = 0

Where \theta, \lambda are scalar fields I want to obtain, F, G operators, x,y coordinates.

I am trying so solve a periodic problem with heat and the second equation describes the gradient of bulk temperature in each cross-section. (the gradient is not constant in my case)

I would be very grateful for your comments.