Introduction Ill-Posedness of Inverse Problems

Inverse problems arise in almost all areas of science and technology, in modeling of problems motivated by various physical and social processes. Most of these models are governed by differential and integral equations. If all the necessary inputs in these models are known, then the solution can be computed and behavior of the physical system under various conditions can be predicted. In terms of differential problems, the necessary inputs include such information as initial or boundary data, coefficients and force term, also shape and size of the domain. If all these data are enough to describe the system adequately, then it is possible to use the mathematical model for studying the physical system.