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."--Provided by publisher.

Cover; Half Title; Title Page; Copyright Page; Preface; Contents; Chapter 1: Inverse Problems for Equations of Parabolic Type; 1.1 Preliminaries; 1.2 The linear inverse problem: recovering a source term; 1.3 The linear inverse problem: the Fredholm solvability; 1.4 The nonlinear coefficient inverse problem: recovering a coefficient depending on x; 1.5 The linear inverse problem: recovering the evolution of a source term; Chapter 2: Inverse Problems for Equations of Hyperbolic Type; 2.1 Inverse problems for x-hyperbolic systems; 2.2 Inverse problems for t-hyperbolic systems

2.3 Inverse problems for hyperbolic equations of the second orderChapter 3: Inverse Problems for Equations of the Elliptic Type; 3.1 Introduction to inverse problems in potential theory; 3.2 Necessary and sufficient conditions for the equality of exterior magnetic potentials; 3.3 The exterior inverse problem for the volume potential with variable density for bodies with a ""star-shaped"" intersection; 3.4 Integral stability estimates for the inverse problem of the exterior potential with constant density

3.5 Uniqueness theorems for the harmonic potential of ""non-star-shaped"" bodies with variable density3.6 T…