Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.
Table of Contents
Inverse problems for equations of parabolic type; inverse problems for equations of hyperbolic type; inverse problems for equations of elliptic type; inverse problems in dynamics of viscous incompressible fluid; some topics from functional analysis and operator theory; abstract inverse problems for first order equations and their applications in mathematical physics; two-point inverse problems for first order equations; inverse problems for equations of second order; applications of the theory of abstract inverse problems to partial differential equations; concluding remarks.
"This book is of course addressed to researchers in inverse problems, but is highly recommend to researchers in direct problems for PDE's who are terrified by the 'bad properties' of inverse problems....The volume builds...a bridge between identification problems for PDE's and Functional Analysis - nowadays well-known to every researcher in PDE's."
---Zentralblatt fur Mathematik, 2000