Methods for Solving Inverse Problems in Mathematical Physics

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. 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.