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1、LectureNotesinMathematics1898Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisHorstReinhardBeyerBeyondPartialDifferentialEquationsOnLinearandQuasi-LinearAbstractHyperbolicEvolutionEquationsABCAuthorHorstReinhardBeyerCenterforComputation&TechnologyL
2、ouisianaStateUniversity330JohnstonHallBatonRougeLA70803USAe-mail:horst@cct.lsu.eduLibraryofCongressControlNumber:2007921690MathematicsSubjectClassification(2000):47J35,47D06,35L60,35L45,35L15ISSNprintedition:0075-8434ISSNelectronicedition:1617-9692ISBN-103-54
3、0-71128-7SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-71128-5SpringerBerlinHeidelbergNewYorkDOI10.1007/978-3-540-71129-2Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,repri
4、nting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissi
5、onforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.com°cSpringer-VerlagBerlinHeidelberg2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc
6、.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.TypesettingbytheauthorandSPiusingaSpringerLATEXmacropackageCoverdesign:WMXDesignGmbH,HeidelbergP
7、rintedonacid-freepaperSPIN:11962175VA41/3100/SPi543210DedicatedtoGodtheFatherPrefaceSemigroupTheoryusesabstractmethodsofOperatorTheorytotreatinitialbound-aryvalueproblemsforlinearandnonlinearequationsthatdescribetheevolutionofasystem.Duetothegeneralityofitsm
8、ethods,theclassofsystemsthatcanbetreatedinthiswayexceedsbyfarthosedescribedbyequationscontainingonlylocaloper-atorsinducedbypartialderivatives,i.e.,PDEs.Inparticular,thatclassincludesthesystemso
