analysis and control of nonlinear infinite dimensional systems(barbu)

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1、AnalysisandControlofNonlinearInfiniteDimensionalSystemsThisisvolume190inMATHEMATICSINSCIENCEANDENGINEERINGEditedbyWilliamF.Ames,GeorgiaInstituteofTechnologyAlistofrecenttitlesinthisseriesappearsattheendofthisvolume.ANALYSISANDCONTROLOFNONLINEARINFINITEDIMENSIONALSYSTEMSViorelBarbuSCHOOLOFMATH

2、EMATICSUNIVERSITYOFIASIIASI,ROMANIAACADEMICPRESS,INC.HarcourtBraceJooanooich,PublishersBostonSanDiegoNewYorkLondonSydneyTokyoTorontoThisbookisprintedonacid-freepaper.@Copyright01993byAcademicPress,Inc.Allrightsreserved.Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,e

3、lectronicormechanical,includingphotocopy,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher.ACADEMICPRESS,INC.1250SixthAvenue,SanDiego,CA92101-4311UnitedKingdomEditionpublishedbyACADEMICPRESSLIMITED24-28OvalRoad,LondonNW17DXLibraryofCongressCatalogi

4、ng-in-PublicationDataBarbu,Viorel.AnalysisandcontrolofnonlinearinfinitedimensionalsystemsViorelBarbu.p.cm.-(Mathematicsinscienceandengineering;v.189)Includesbibliographicalreferencesandindex.ISBN0-12-078145-X1.Controltheory.2.Mathematicaloptimization.3.Nonlinearoperators.I.Title.11.Series.QA4

5、02.3.B3431993003'.5-d~2092-2851CIPPRINTEDINTHEUNITEDSTATESOFAMERICA92939495EB987654321ContentsPrefaceviiNotationandSymbolsixChapter1Preliminaries11.1TheDualityMapping11.2CompactMappingsinBanachSpaces51.3AbsolutelyContinuousFunctionswithValuesinBanachSpaces91.4LinearDifferentialEquationsinBana

6、chSpaces17Chapter2NonlinearOperatorsofMonotoneType352.1MaximalMonotoneOperators352.2GeneralizedGradients(SubpotentialOperators)572.3AccretiveOperatorsinBanachSpaces99BibliographicalNotesandRemarks123Chapter3ControlledEllipticVariationalInequalities1253.1EllipticVariationalInequalities.Existen

7、ceTheory1253.2OptimalControlofEllipticVariationalInequalities148BibliographicalNotesandRemarks196Chapter4NonlinearAccretiveDifferentialEquations1994.1TheBasicExistenceResults1994.2ApproximationandConvergenceofNonlinearEvolutionsandSemigroups2