Neumann B.C. with dependance on value at boundary

Dear all,
I am trying to implement a boundary condition where the rate of change of my function at the boundary depends on the value of the function at this boundary in a nonlinear way. How can I implement his?
As far as I understand, I can use the expression
∂nu = g : -int1d(Th)( g*w)
for Neumann boundary conditions. But what if g itself depends on the value of the unknown function u?
Thank you

Dear Lysandros,
Are you looking for the Robin boundary condition (g(u) linear with u)? Then you may start here: Laplace eigenproblem with Robin boundary condition
If the Robin BC is nonlinear, you may have to implement a nonlinear solution of your problem.

Dear Vincent, thanks for your reply. Actually, I want to model thermal radiation from the surface of a plate. Therefore, the local gradient at the boundary should be du/dx=u^4, since radiation scales with the fourth power of the surface temperature. Would this fall in the category of a Robin boundary condition? Am I on a good road if use the int1d term?
Kins regards

Sorry for the very late reply. Your case is clearly nonlinear then, so you need to implement a nonlinear solution in my understanding.