Coupling models or coupling codes: two examples where the coupled model has better properties than each model.

In a simple setting (1d in space), a model of porous media (which is characterized by a degenerate parabolic equation) is coupled with the behavior of the medium, the resulting system is a non degenerate heat equation. Similarly, the diffusion equation of neutronics, which coefficients depend on the local temperature of the nuclear core, is (classically) an eigenvalue problem, with infinitely many eigenvalues. Coupled with the equation for the local temperature yields a unique solution.