Identifiability of distributed physical parameters in diffusive-like systems

Modelling of 1D diffusive-like systems leads to a parabolic partial differential equation. Since it is usually difficult to measure the physical parameters of the system (a and b), whereas it is easier to measure u (potential) and f (source term), a and b are deduced from u and f by solving an ill-posed inverse problem. The physical parameters are said to be identifiable if different parameter distributions correspond to different potential distributions. Identifiability is equivalent to the uniqueness of the solution of the inverse problem in its direct formulation.