Springer.Inverse.Problems.Mathematical.and.Analytical.Techniques.[Springer.2005]

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

2、onsofPartialDifferentialEquationswithApplicationsS.V.MeleshkoTheFastSolutionofBoundaryIntegralEquationsS.RjasanowandO.SteinbachStochasticDifferentialEquationswithApplicationsR.SituINVERSEPROBLEMSMATHEMATICALANDANALYTICALTECHNIQUESWITHAPPLICATIONSTOENGINEERINGALEXANDERG.RAMMSpringereBoo

3、kISBN:0-387-23218-4PrintISBN:0-387-23195-1©2005SpringerScience+BusinessMedia,Inc.Print©2005SpringerScience+BusinessMedia,Inc.BostonAllrightsreservedNopartofthiseBookmaybereproducedortransmittedinanyformorbyanymeans,electronic,mechanical,recording,orotherwise,withoutwrittenconsentfromth

4、ePublisherCreatedintheUnitedStatesofAmericaVisitSpringer'seBookstoreat:http://ebooks.springerlink.comandtheSpringerGlobalWebsiteOnlineat:http://www.springeronline.comToLubaandOlgaThispageintentionallyleftblankCONTENTSForewordxvPrefacexvii1.Introduction11.1Whyareinverseproblemsinteresti

5、ngandpracticallyimportant?11.2Examplesofinverseproblems21.2.1Inverseproblemsofpotentialtheory21.2.2Inversespectralproblems21.2.3Inversescatteringproblemsinquantumphysics;findingthepotentialfromtheimpedancefunction21.2.4Inverseproblemsofinterestingeophysics31.2.5Inverseproblemsforthehea

6、tandwaveequations31.2.6Inverseobstaclescattering41.2.7Findingsmallsubsurfaceinhomogeneitiesfromthemeasurementsofthescatteredfieldonthesurface51.2.8Inverseproblemofradiomeasurements51.2.9Impedancetomography(inverseconductivity)problem51.2.10Tomographyandotherintegralgeometryproblems51.2

7、.11Inverseproblemswith“incompletedata”61.2.12ThePompeiuproblem,Schiffer’sconjecture,andinverseproblemofplasmatheory71.2.13Multidimensionalinversepotentialscattering81.2.14Ground-penetratingradar81.2.15Ageometricalinverseproblem91.2.16Inversesourceproblems10viiiContents1.2.17Identific