Springer.Inverse.Problems.Mathematical.and.Analytical.Techniques.With.Applications.To.Engineering.2005

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

2、ctingExactSolutionsofPartialDifferentialEquationswithApplicationsS.V.MeleshkoTheFastSolutionofBoundaryIntegralEquationsS.RjasanowandO.SteinbachStochasticDifferentialEquationswithApplicationsR.SituINVERSEPROBLEMSMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINE

3、ERINGALEXANDERG.RAMMSpringereBookISBN:0-387-23218-4PrintISBN:0-387-23195-1©2005SpringerScience+BusinessMedia,Inc.Print©2005SpringerScience+BusinessMedia,Inc.BostonAllrightsreservedNopartofthiseBookmaybereproducedortransmittedinanyformorbyanymeans,electronic,mechanical,r

4、ecording,orotherwise,withoutwrittenconsentfromthePublisherCreatedintheUnitedStatesofAmericaVisitSpringer'seBookstoreat:http://ebooks.springerlink.comandtheSpringerGlobalWebsiteOnlineat:http://www.springeronline.comToLubaandOlgaThispageintentionallyleftblankCONTENTSForew

5、ordxvPrefacexvii1.Introduction11.1Whyareinverseproblemsinterestingandpracticallyimportant?11.2Examplesofinverseproblems21.2.1Inverseproblemsofpotentialtheory21.2.2Inversespectralproblems21.2.3Inversescatteringproblemsinquantumphysics;findingthepotentialfromtheimpedancef

6、unction21.2.4Inverseproblemsofinterestingeophysics31.2.5Inverseproblemsfortheheatandwaveequations31.2.6Inverseobstaclescattering41.2.7Findingsmallsubsurfaceinhomogeneitiesfromthemeasurementsofthescatteredfieldonthesurface51.2.8Inverseproblemofradiomeasurements51.2.9Impe

7、dancetomography(inverseconductivity)problem51.2.10Tomographyandotherintegralgeometryproblems51.2.11Inverseproblemswith“incompletedata”61.2.12ThePompeiuproblem,Schiffer’sconjecture,andinverseproblemofplasmatheory71.2.13Multidimensionalinversepotentialscattering81.2.14Gro

8、und-penetratingradar81.2.15Ageometricalinverseproblem91.2.16Inversesourceproblems10viiiContents1.2.17Identific