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[美] 艾赛科威 (Victor Isakov) 著 / 世界图书出版公司 / 2014-03 / 平装
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上书时间2020-10-21
偏微分方程中的逆问题(第2版,英文版)
《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。
PrefacetotheSecondEditionPrefacetotheFirstEditionChapter1InverseProblems1.1Theinverseproblemofgravimetry1.2Theinverseconductivityproblem1.3Inversescattering1.4Tomographyandtheinverseseismicproblem1.5InversespectralproblemsChapter2Ⅱ-PosedProblemsandRegularization2.1Well-andill-posedproblems2.2Conditionalcorrectness:Regularization2.3Constructionofregularizers2.4Convergenceofregularizationalgorithms2.5IterativealgorithmsChapter3UniquenessandStabilityintheCauchyProblem3.!Thebackwardparabolicequation3.2GeneralCarlemanestimatesandtheCauchyproblem3.3Ellipticandparabolicequations3.4HyperbolicandSchrodingerequations3.5Systemsofpartialdifferentialequations3.6OpenproblemsChapter4EllipticEquations:SingleBoundaryMeasurements4.0Resultsonellipticboundaryvalueproblems4.1Inversegravimetry4.2Reconstructionoflower-orderterms4.3Theinverseconductivityproblem4.4Methodsofthetheoryofonecomplexvariable1.6Linearizationofthecoefficientsproblem1.7Someproblemsofdetectionofdefects1.8OpenproblemsChapter5EllipticEquations:ManyBoundaryMeasurements2.6TheDirichlet-to-Neumannmap2.7Boundaryreconstruction2.8ReconstructioninQ2.9CompletenessofproductsofsolutionsofPDE2.10Recoveryofseveralcoefficients2.11Theplanecase2.12Nonlinearequations2.13Discontinuousconductivities2.14Maxwell’sandelasticitysystems2.15OpenproblemsChapter6ScatteringProblems3.7DirectScattering3.8FromAtonearfield3.9Scatteringbyamedium3.10Scatteringbyobstacles3.11OpenproblemsChapter7IntegralGeometryandTomography4.5TheRadontransformanditsinverse4.6Theenergyintegralmethods4.7Boman'scounterexample4.8Thetransportequation4.9OpenproblemsChapter8HyperbolicProblems8.0Introduction8.1Theone-dimensionalcase8.2Singleboundarymeasurements8.3Manymeasurements:useofbeamsolutions8.4Manymeasurements:methodsofboundarycontrol8.5Recoveryofdiscontinuityofthespeedofpropagation8.6OpenproblemsChapter9Inverseparabolicproblems9.0Introduction9.1Finaloverdetermination9.2Lateraloverdetermination:singlemeasurements9.3Theinverseproblemofoptionpricing9.4Lateraloverdetermination:manymeasurements……Chapter10SomeNumericalMethods
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