Springer.Inverse.Problems.(2005)

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1、INVERSEPROBLEMSMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGAlanJeffrey,ConsultingEditorPublished:InverseProblemsA.G.RammSingularPerturbationTheoryR.S.JohnsonForthcoming:MethodsforConstructingExactSolutionsofPartialD

2、ifferentialEquationswithApplicationsS.V.MeleshkoTheFastSolutionofBoundaryIntegralEquationsS.RjasanowandO.SteinbachStochasticDifferentialEquationswithApplicationsR.SituINVERSEPROBLEMSMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGALEXANDERG.RAMMSpringereBookISBN:0-387-23218-4PrintIS

3、BN:0-387-23195-1©2005SpringerScience+BusinessMedia,Inc.Print©2005SpringerScience+BusinessMedia,Inc.BostonAllrightsreservedNopartofthiseBookmaybereproducedortransmittedinanyformorbyanymeans,electronic,mechanical,recording,orotherwise,withoutwrittenconsentfromthePublisherCreatedintheUnitedStatesofAme

4、ricaVisitSpringer'seBookstoreat:http://ebooks.springerlink.comandtheSpringerGlobalWebsiteOnlineat:http://www.springeronline.comToLubaandOlgaThispageintentionallyleftblankCONTENTSForewordxvPrefacexvii1.Introduction11.1Whyareinverseproblemsinterestingandpracticallyimportant?11.2Examplesofinverseprobl

5、ems21.2.1Inverseproblemsofpotentialtheory21.2.2Inversespectralproblems21.2.3Inversescatteringproblemsinquantumphysics;findingthepotentialfromtheimpedancefunction21.2.4Inverseproblemsofinterestingeophysics31.2.5Inverseproblemsfortheheatandwaveequations31.2.6Inverseobstaclescattering41.2.7Findingsmal

6、lsubsurfaceinhomogeneitiesfromthemeasurementsofthescatteredfieldonthesurface51.2.8Inverseproblemofradiomeasurements51.2.9Impedancetomography(inverseconductivity)problem51.2.10Tomographyandotherintegralgeometryproblems51.2.11Inverseproblemswith“incompletedata”61.2.12ThePompeiuproblem,Schiffer’sconje

7、cture,andinverseproblemofplasmatheory71.2.13Multidimensionalinversepotentialscattering81.2.14Ground-penetratingradar81.2.15Ageometricalinverseproblem91.2.16Inversesourceproblems10viiiContents1.2.17Identific