4. Examples of incorrectly posed inverse problems

4.1 A simple case of inversion: stationary 1D conduction in a plane wall. Example 1

Here we consider the problem of permanent unidirectional heat transfer in a homogeneous wall. We know the exact temperature T _e on the face x = e and we measure the temperature y from a sensor implanted at a depth x _c in the medium. Using these two pieces of information and knowing the exact values of the conductivity λ and the thickness e of the wall, we seek to estimate (figure 6 a ) :