拟线性双曲系统的能控性与能观性(国内英文版)

《拟线性双曲系统的能控性与能观性(英文版)》是由高等教育出版社出版的。

《拟线性双曲系统的能控性与能观性(英文版)》内容简介：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