Identifiability of Piecewise Constant Conductivity in a Heat Conduction Process

We study the identification and identifiability problems for heat conduction in a nonhomogeneous rod. The identifiability results are established for two different sets of observations. Given a sequence of distributed type observations, the identifiability is proved for conductivities in a piecewise smooth class of functions. In the case of observations taken at finitely many points the identifiability is established for piecewise constant conductivities. Such conductivities can be uniquely identified using the proposed marching algorithm.