拟线性双曲系统的能控性与能观性(作者签名书)

Thecontrollabilityandobservabilityareofgreatimportanceinboththeoryandapplications.Acompletetheoryhasbeenestablishedforlinearhyperbolicsystems，inparticular，forlinearwaveequations.Therehavealsobeensomeresultsforsemilinearwaveequations.Forquasilinearhyperbolicsystemsthathavenumerousapplicationsinmechanics，physicsandotherappliedsciences，however，veryfewresultsareavailableevenwithspacedimensionone.

Thismonographisbasedmainlyontheresultsobtainedbytheauthorandhiscollaboratorsinrecentyears.Bymea~softhetheoryonthesemi-globalclassicalsolution，asimpleanddirectconstructivemethodispresentedinasystematicwaytogetboththecontrollabilityandobservabilityintheframeworkofclassicalsolutionsforgeneralfirstorder1-Dquasilinearhyperbolicsystemswithgeneralnonlinearboundaryconditions.Correspondingapplicationsaregivenfor1-Dquasilinearwaveequationsandforunsteadyflowsinatree-likenetworkofopencanals，respectively.Morethanonehundredrelatedreferencesareprovided.

Thisbookwith11chaptersisself-contained.Anappendixisespeciallywrittenforthosereaderswhoarenotfamiliarwithquasilinearhyperbolicsystems.

Thisbookwillbeofbenefittoscholarsandgraduatestudentsinappliedmathematicsandappliedsciences.Itmaybeusedasatextbookoramainreferenceforgraduatestudentsincorrespondingareas.

Introduction
1.1ExactControllability
1.2ExactObservability
1.3"Duality"BetweenControllabilityandObservability
1.4ExactBoundaryControllabilityandExactBoundaryObservabilityfor1-DQuasilinearWaveEquations
1.5ExactBoundaryControllabilityandExactBoundaryObservabilityofUnsteadyFlowsinaTree-LikeNetworkofOpenCanals
1.6NonautonomousHyperbolicSystems
1.7NotesontheOne-SidedExactBoundaryControllabilityandObservability
2Semi-GlobalC1SolutionsforFirstOrderQuasilinearHyperbolicSystems
2.1Introduction
2.2EquivalenceofProblemIandProblemII
2.3LocalC1SolutiontotheMixedInitial-BoundaryValueProblem
2.4Semi-GlobalC1SolutiontotheMixedInitial-BoundaryValueProblem
2.5Remarks
3ExactControllabilityforFirstOrderQuasilinearHyperbolicSystems
3.1IntroductionandMainResults
3.2FrameworkofResolution
3.3Two-SidedControl——ProofofTheorem3.1
3.4One-SidedControl——ProofofTheorem3.2
3.5Two-SidedControlwithLessControls——ProofofTheorem3.3.
3.6ExactControllabilityforFirstOrderQuasilinearHyperbolicSystemswithZeroEigenvalues
4ExactObservabilityforFirstOrderQuasilinearHyperbolicSystems
4.1IntroductionandMainResults
4.2Two-SidedObservation——ProofofTheorem4.1
4.3One-SidedObservation——ProofofTheorem4.2
4.4Two-SidedObservationwithLessObservedValues——ProofofTheorem4.3
4.5ExactObservabilityforFirstOrderQuasilinearHyperbolicSystemswithZeroEigenvalues
4.6"Duality"BetweenControllabilityandObservabilityforFirstOrderQuasilinearHyperbolicSystems
5ExactBoundaryControllabilityforQuasilinearWaveEquations
5.1IntroductionandMainResults
5.2Semi-GlobalC2Solutionfor1-DQuasilinearWaveEquations
5.3Two-SidedControl——ProofofTheorem5.1
5.4One-SidedControl——ProofofTheorem5.2
5.5Remarks
6ExactBoundaryObservabilityforQuasilinearWaveEquations
6.1Introduction
6.2Semi-GlobalC2Solutionfor1-DQuasilinearWaveEquations（Continued）
6.3ExactBoundaryObservability
6.4"Duality"BetweenControllabilityandObservabilityforQuasilinearWaveEquations
7ExactBoundaryControllabilityofUnsteadyFlowsinaTree-LikeNetworkofOpenCanals
7.1Introduction
7.2Preliminaries
7.3ExactBoundaryControllabilityofUnsteadyFlowsinaSingleOpenCanal
7.4ExactBoundaryControllabilityforQuasilinearHyperbolicSystemsonaStar-LikeNetwork
7.5ExactBoundaryControllabilityofUnsteadyFlowsinaStar-LikeNetworkofOpenCanals
7.6ExactBoundaryControllabilityofUnsteadyFlowsinaTree-LikeNetworkofOpenCanals
7.7Remarks
8ExactBoundaryObservabilityofUnsteadyFlowsinaTree-LikeNetworkofOpenCanals
8.1Introduction
8.2Preliminaries
8.3ExactBoundaryObservabilityofUnsteadyFlowsinaSingleOpenCanal
8.4ExactBoundaryObservabilityofUnsteadyFlowsina
Star-LikeNetworkofOpenCanals8.5ExactBoundaryObservabilityofUnsteadyFlowsinaTree-LikeNetworkofOpenCanals
8.6"Duality"BetweenControllabilityandObservabilityinaTree-LikeNetworkofOpenCanals
9ControllabilityandObservabilityforNonautonomousHyperbolicSystems
9.1Introduction
9.2Two-SidedControl
9.3One-SidedControl
9.4Two-SidedObservation
9.5One-SidedObservation
9.6Remarks
10NoteontheOne-SidedExactBoundaryControllabilityforFirstOrderQuasilinearHyperbolicSystems
10.1Introduction
10.2ReductionoftheProblem
10.3Semi-GlobalC2SolutiontoaClassofSecondOrderQuasilinearHyperbolicEquations
10.4One-SidedExactBoundaryControllabilityforaClassof
SecondOrderQuasilinearHyperbolicEquations
11NoteontheOne-SidedExactBoundaryObservabilityforFirstOrderQuasilinearHyperbolicSystems
11.1Introduction
11.2ReductionoftheProblem
11.3ProofofTheorem11.1
11.4"Duality"BetweenControllabilityandObservability
AppendixA：AnIntroductiontoQuasilinearHyperbolicSystems
A.1DefinitionofQuasilinearHyperbolicSystem
A.2CharacteristicFormofHyperbolicSystem
A.3ReducibleQuasilinearHyperbolicSystem.RiemannInvariants
A.4Blow-UpPhenomenon
A.5CauchyProblem
A.6MixedInitial-BoundaryValueProblem
A.7DecompositionofWaves
References
Index