《偏微分方程中的逆問題（第2版）》是2014年世界圖書出版公司出版的著作，作者是[美] 艾賽科威（Victor Isakov）。
基本介紹
- 書名：《偏微分方程中的逆問題（第2版）》
- 作者：[美]艾賽科威（Victor Isakov）
- 出版社：世界圖書出版公司
- 出版時間：2014-03-01
內容簡介,目錄,
《偏微分方程中的逆問題（第2版，英文版）》全面講述了目前偏微分方程中逆問題的理論和數值方面。逆問題這個話題十分寬泛，並且得到了眾多科學家和工程人員的青睞。這是第二版，包括了逆問題領域的進展，給出了理論和計算方法，強調觀點和技巧。書中也體現了和第一版的不同，做了許多修訂，內容更加充實，增加了如偽凸的概念，簡化了證明。新材料的增加反應了逆問題理論的進展。《偏微分方程中的逆問題（第2版）》對象是偏微分方程及其套用領域的數學工作者、物理學家、幾何物理學家和工程人員。
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
