ABSTRACT
In this chapter, the unknown conductivity is considered to be mainly space-dependent charaterising a functionally-graded or heterogeneous medium. First, the determination of a spatially dependent permeability of a one-dimensional reservoir from measurements of the permeability itself at a few locations along with pressure data is considered. Second, the recovery of a discontinuous anisotropic conductivity is analyzed and the size of inclusion is estimated. Third, a special type of layered and time-dependent orthotropic conductivity with the main diagonal components independent of one space variable is considered. Then, the conductivity components can be taken outside the divergence operator and the inverse problem that is investigated requires reconstructing one or two components of such orthotropic conductivity tensor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary of a rectangular conductor.
