本书全面讲述了目前偏微分方程中逆问题的理论和数值方面。逆问题这个话题十分宽泛，并且得到了众多科学家和工程人员的青睐。这是第二版，包括了逆问题领域的最新进展，给出了理论和计算方法，强调最新观点和技巧。书中也体现了和第一版的不同，做了许多修订，内容更加充实，增加了如伪凸的概念，简化了证明。新材料的增加反应了逆问题理论的最新进展。本书对象是偏微分方程及其应用领域的数学工作者、物理学家、几何物理学家和工程人员。
Preface to the Second Edition Preface to the First Edition
Chapter 1 Inverse Problems
1.1 The inverse problem of gravimetry
1.2 The inverse conductivity problem
1.3 Inverse scattering
1.4 Tomography and the inverse seismic problem
1.5 Inverse spectral problems
Chapter 2 Ⅱ-Posed Problems and Regularization
2.1 Well- and ill-posed problems
2.2 Conditional correctness: Regularization
2.3 Construction of regularizers
2.4 Convergence of regularization algorithms
2.5 Iterative algorithms
Chapter 3 Uniqueness and Stability in the Cauchy Problem
3.! The backward parabolic equation
3.2 General Carleman estimates and the Cauchy problem
3.3 Elliptic and parabolic equations
3.4 Hyperbolic and Schrodinger equations
3.5 Systems of partial differential equations
3.6 Open problems
Chapter 4 Elliptic Equations: Single Boundary Measurements
4.0 Results on elliptic boundary value problems
4.1 Inverse gravimetry
4.2 Reconstruction of lower-order terms
4.3 The inverse conductivity problem
4.4 Methods of the theory of one complex variable
1.6 Linearization of the coefficients problem
1.7 Some problems of detection of defects
1.8 Open problems
Chapter 5 Elliptic Equations: Many Boundary Measurements
2.6 The Dirichlet-to-Neumann map
2.7 Boundary reconstruction
2.8 Reconstruction in Q
2.9 Completeness of products of solutions of PDE
2.10 Recovery of several coefficients
2.11 The plane case
2.12 Nonlinear equations
2.13 Discontinuous conductivities
2.14 Maxwell’s and elasticity systems
2.15 Open problems
Chapter 6 Scattering Problems
3.7 Direct Scattering
3.8 From A to near field
3.9 Scattering by a medium
3.10 Scattering by obstacles
3.11 Open problems
Chapter 7 Integral Geometry and Tomography
4.5 The Radon transform and its inverse
4.6 The energy integral methods
4.7 Boman's counterexample
4.8 The transport equation
4.9 Open problems
Chapter 8 Hyperbolic Problems
8.0 Introduction
8.1 The one-dimensional case
8.2 Single boundary measurements
8.3 Many measurements: use of beam solutions
8.4 Many measurements: methods of boundary control
8.5 Recovery of discontinuity of the speed of propagation
8.6 Open problems
Chapter 9 Inverse parabolic problems
9.0 Introduction
9.1 Final overdetermination
9.2 Lateral overdetermination: single measurements
9.3 The inverse problem of option pricing
9.4 Lateral overdetermination: many measurements
……
Chapter 10 Some Numerical Methods
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