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偏微分方程中的逆问题 第2版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）艾赛科威（IsakovV.）著 著
- 出版社： 北京;西安：世界图书出版公司
- ISBN：9787510070235
- 出版时间：2014
- 标注页数：347页
- 文件大小：60MB
- 文件页数：362页
- 主题词：偏微分方程－逆问题－研究－英文
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图书目录
Chapter 1 Inverse Problems1
1.1 The inverse problem of gravimetry1
1.2 The inverse conductivity problem5
1.3 Inverse scattering7
1.4 Tomography and the inverse seismic problem10
1.5 Inverse spectral problems14
Chapter 2 Ill-Posed Problems and Regularization20
2.1 Well- and ill-posed problems20
2.2 Conditional correctness:Regularization23
2.3 Construction of regularizers26
2.4 Convergence of regularization algorithms33
2.5 Iterative algorithms37
Chapter 3 Uniqueness and Stability in the Cauchy Problem41
3.1 The backward parabolic equation42
3.2 General Carleman estimates and the Cauchy problem51
3.3 Elliptic and parabolic equations57
3.4 Hyperbolic and Schr？dinger equations65
3.5 Systems of partial differential equations80
3.6 Open problems86
Chapter 4 Elliptic Equations:Single Boundary Measurements89
4.0 Results on elliptic boundary value problems89
4.1 Inverse gravimetry92
4.2 Reconstruction of lower-order terms97
4.3 The inverse conductivity problem102
4.4 Methods of the theory of one complex variable111
4.5 Linearization of the coefficients problem116
4.6 Some problems of detection of defects119
4.7 Open problems125
Chapter 5 Elliptic Equations:Many Boundary Measurements127
5.0 The Dirichlet-to-Neumann map127
5.1 Boundary reconstruction130
5.2 Reconstruction in Ω134
5.3 Completeness of products of solutions of PDE138
5.4 Recovery of several coefficients143
5.5 The plane case149
5.6 Nonlinear equations154
5.7 Discontinuous conductivities160
5.8 Maxwell's and elasticity systems166
5.9 Open problems170
Chapter 6 Scattering Problems173
6.0 Direct Scattering173
6.1 From A to near field176
6.2 Scattering by a medium180
6.3 Scattering by obstacles184
6.4 Open problems190
Chapter 7 Integral Geometry and Tomography192
7.1 The Radon transform and its inverse192
7.2 The energy integral methods201
7.3 Boman's counterexample205
7.4 The transport equation208
7.5 Open problems215
Chapter 8 Hyperbolic Problems218
8.0 Introduction218
8.1 The one-dimensional case221
8.2 Single boundary measurements229
8.3 Many measurements:use of beam solutions236
8.4 Many measurements:methods of boundary control243
8.5 Recovery of discontinuity of the speed of propagation249
8.6 Open problems253
Chapter 9 Inverse parabolic problems255
9.0 Introduction255
9.1 Final overdetermination259
9.2 Lateral overdetermination:single measurements264
9.3 The inverse problem of option pricing270
9.4 Lateral overdetermination:many measurements275
9.5 Discontinuous principal coefficient and recovery of a domain279
9.6 Nonlinear equations288
9.7 Interior sources293
9.8 Open problems295
Chapter 10 Some Numerical Methods297
10.1 Linearization298
10.2 Variational regularization of the Cauchy problem303
10.3 Relaxation methods308
10.4 Layer-stripping310
10.5 Range test algorithms313
10.6 Discrete methods318
Appendix.Functional Spaces321
References324
Index343