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內容簡介

　　《偏微分方程中的逆問題（第2版，英文版）》全麵講述瞭目前偏微分方程中逆問題的理論和數值方麵。逆問題這個話題十分寬泛，並且得到瞭眾多科學傢和工程人員的青睞。這是第二版，包括瞭逆問題領域的進展，給齣瞭理論和計算方法，強調觀點和技巧。書中也體現瞭和第一版的不同，做瞭許多修訂，內容更加充實，增加瞭如僞凸的概念，簡化瞭證明。新材料的增加反應瞭逆問題理論的進展。《偏微分方程中的逆問題（第2版）》對象是偏微分方程及其應用領域的數學工作者、物理學傢、幾何物理學傢和工程人員。

內頁插圖

目錄

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

前言/序言

偏微分方程中的逆問題（第2版，英文版） [Inverse Problems for Partial Differential Equations(Second Edition)] 下載 mobi epub pdf txt 電子書

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