偏微分方程中的逆问题（第2版，英文版）

图书标准信息

• 作者 [美]艾赛科威（Victor Isakov） 著
• 出版社 世界图书出版公司
• 出版时间 2014-03
• 版次 2
• ISBN 9787510070235
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 344页
• 正文语种 英语

【内容简介】

　　《偏微分方程中的逆问题（第2版，英文版）》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。《偏微分方程中的逆问题（第2版）》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。

【目录】

PrefacetotheSecondEditionPrefacetotheFirstEdition
Chapter1InverseProblems
1.1Theinverseproblemofgravimetry
1.2Theinverseconductivityproblem
1.3Inversescattering
1.4Tomographyandtheinverseseismicproblem
1.5Inversespectralproblems

Chapter2Ⅱ-PosedProblemsandRegularization
2.1Well-andill-posedproblems
2.2Conditionalcorrectness:Regularization
2.3Constructionofregularizers
2.4Convergenceofregularizationalgorithms
2.5Iterativealgorithms

Chapter3UniquenessandStabilityintheCauchyProblem
3.!Thebackwardparabolicequation
3.2GeneralCarlemanestimatesandtheCauchyproblem
3.3Ellipticandparabolicequations
3.4HyperbolicandSchrodingerequations
3.5Systemsofpartialdifferentialequations
3.6Openproblems

Chapter4EllipticEquations:SingleBoundaryMeasurements
4.0Resultsonellipticboundaryvalueproblems
4.1Inversegravimetry
4.2Reconstructionoflower-orderterms
4.3Theinverseconductivityproblem
4.4Methodsofthetheoryofonecomplexvariable
1.6Linearizationofthecoefficientsproblem
1.7Someproblemsofdetectionofdefects
1.8Openproblems

Chapter5EllipticEquations:ManyBoundaryMeasurements
2.6TheDirichlet-to-Neumannmap
2.7Boundaryreconstruction
2.8ReconstructioninQ
2.9CompletenessofproductsofsolutionsofPDE
2.10Recoveryofseveralcoefficients
2.11Theplanecase
2.12Nonlinearequations
2.13Discontinuousconductivities
2.14Maxwell’sandelasticitysystems
2.15Openproblems

Chapter6ScatteringProblems
3.7DirectScattering
3.8FromAtonearfield
3.9Scatteringbyamedium
3.10Scatteringbyobstacles
3.11Openproblems

Chapter7IntegralGeometryandTomography
4.5TheRadontransformanditsinverse
4.6Theenergyintegralmethods
4.7Boman'scounterexample
4.8Thetransportequation
4.9Openproblems

Chapter8HyperbolicProblems
8.0Introduction
8.1Theone-dimensionalcase
8.2Singleboundarymeasurements
8.3Manymeasurements:useofbeamsolutions
8.4Manymeasurements:methodsofboundarycontrol
8.5Recoveryofdiscontinuityofthespeedofpropagation
8.6Openproblems

Chapter9Inverseparabolicproblems
9.0Introduction
9.1Finaloverdetermination
9.2Lateraloverdetermination:singlemeasurements
9.3Theinverseproblemofoptionpricing
9.4Lateraloverdetermination:manymeasurements
……
Chapter10SomeNumericalMethods