ABSTRACT
This chapter considers inverse problems for partial differential equations (Laplace's, Stokes, biharmonic and heat) in which boundary conditions on a portion of the boundary of the solution domain are under-prescribed. This situations occur in physical problems where parts of the boundary of a specimen are either inaccessible to measurement, e.g. buried or hidden, or they are in contact with a hostile environment, e.g. high temperatures/high pressures. The missing boundary data information is compensated for by over-prescribed boundary conditions (Cauchy data) on an accessible and friendly sub-portion of the boundary. Because only boundary information is considered, these Cauchy inverse problems are typically associated with non-destructive testing of materials. Several iterative and non-iterative regularising algorithms are described and numerically illustrated.
