力学和物理学中的无限维动力系统 第2版
出版时间:
2000-06
版次:
1
ISBN:
9787506247160
定价:
100.00
装帧:
平装
开本:
24开
纸张:
胶版纸
页数:
648页
-
Sincepublicationofthefirsteditionofthisbookin1988，thestudyofdynamicalsystemsofinfinitedimensionhasbeenaveryactiveareainpureandappliedmathematics;newresultsincludethestudyoftheexistenceofattractorsforalargenumberofsystemsinmathematicalphysicsandmechanics;lowerandupperestimatesonthedimensionoftheattractors;approximationofattractors;inertialmanifoldsandtheirapproximation.Thestudyofmultilevelnumericalmethodsstemmingfromdynamicalsystemstheoryhasalsodevelopedasasubjectonitsown.Finally，intermediateconceptsbetweenattractorsandinertialmanifoldshavealsobeenintroduced，inparticulartheconceptofinertialsets.
本书为英文版。 PrefacetotheSecondEdition
PrefacetotheFirstEdition
GENERALINTRODUCTION.
TheUser‘sGuide
Introduction
1.MechanismandDescriptionofChaos.TheFinite-DimensionalCase
2.MechanismandDescriptionofChaos.TheInfinite-DimensionalCase
3.TheGlobalAttractor.ReductiontoFiniteDimension
4.RemarksontheComputationalAspect
5.TheUser‘sGuide
CHAPTERⅠGeneralResultsandConceptsonInvariantSetsandAttractors
Introduction
1.Semigroups，InvariantSets，andAttractors
2.ExamplesinOrdinaryDifferentialEquations
3.FractalInterpolationandAttractors
CHAPTERⅡElementsofFunctionalAnalysis
Introduction
1.FunctionSpaces
2.LinearOperators
3.LinearEvolutionEquationsoftheFirstOrderinTime
4.LinearEvolutionEquationsoftheSecondOrderinTime
CHAPTERⅢAttractorsoftheDissipativeEvolutionEquationoftheFirstOrderinTime:Reaction-DiffusionEquations.FluidMechanicsandPatternFormationEquationsIntroduction
1.Reaction-DiffusionEquations
2.Navier-StokesEquations（n=2）
3.OtherEquationsinFluidMechanics
4.SomePatternFormationEquations
5.SemilinearEquations
6.BackwardUniqueness
CHAPTERⅣAttractorsofDissipativeWaveEquations
Introduction
1.LinearEquations:SummaryandAdditionalResults
2.TheSine-GordonEquation
3.ANonlinearWaveEquationofRelativisticQuantumMechanics
4.AnAbstractWaveEquation
5.TheGinzburg-LandauEquation
6.WeaklyDissipativeEquations.I.TheNonlinearSchr6dingerEquation
7.WeaklyDissipativeEquationsII.TheKorteweg-DeVriesEquation
8.UnboundedCase:TheLackofCompactness
9.RegularityofAttractors
10.StabilityofAttractors
CHAPTERⅤLyapunovExponentsandDimensionofAttractors
Introduction
1.LinearandMultilinearAlgebra
2.LyapunovExponentsandLyapunovNumbers
3.HausdorffandFractalDimensionsofAttractors
CHAPTERⅥExplicitBoundsontheNumberofDegreesofFreedomandtheDimensionofAttractorsofSomePhysicalSystems
Introduction
1.TheLorenzAttractor
2.Reaction-DiffusionEquations
3.Navier-StokesEquations（n=2）
4.OtherEquationsinFluidMechanic
5.PatternFormationEquations
6.DissipativeWaveEquations
7.TheGinzburg-LandauEquation
8.DifferentiabilityoftheSemigroup
CHAPTER ⅦNon-Well-PosedProblems,UnstableManifolds,LyapunovFunctions,andLowerBoundsonDimensions
Introduction
PARTA:NoN-WELL-POSEDPROBLEMS
1.DissipativityandWellPosedness
2.EstimateofDimensionforNon-Well-PosedProblems:ExamplesinFluidDynamics
PARTB:UNSTABLEMANIFOLDS,LYAPUNOVFUNCTIONS,ANDLOWERBOUNDSONDIMENSIONS
3.StableandUnstableManifolds
4.TheAttractorofaSemigroupwithaLyapunovFunction
5.LowerBoundsonDimensionsofAttractors:AnExample
CHAPTERⅧTheConeandSqueezingProperties.InertialManifolds
Introduction
1.TheConeProperty
2.ConstructionofanInertialManifold:DeScriptionoftheMethod
3.ExistenceofanInertialManifold
4.Examples
5.ApproximationandStabilityoftheInertialManifoldwithRespecttoPerturbations
CHAPTERⅨInertialManifoldsandSlowManifolds.TheNon-Self-AdjointCase
Introduction
1.TheFunctionalSetting
2.TheMainResultLipschitzCase
3.ComplementsandApplications
4.InertialManifoldsandSlowManifolds
CHAPTERⅩApproximationofAttractorsandInertialManifolds.ConvergentFamiliesofApproximateInertialManifolds
Introduction
1.ConstructionoftheManifolds
2.ApproximationofAttractors
3.ConvergentFamiliesofApproximateInertialManifolds
APPENDIXCollectiveSobolevInequalities
Introduction
1.NotationsandHypotheses
2.SpectralEstimatesforSchrodinger-TypeOperators
3.GeneralizationoftheSobolev-Lieb-ThirringInequalityⅠ
4.GeneralizationoftheSobolev-Lieb-ThirringInequalityⅡ
5.Examples
Bibliography
Index
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内容简介:
Sincepublicationofthefirsteditionofthisbookin1988，thestudyofdynamicalsystemsofinfinitedimensionhasbeenaveryactiveareainpureandappliedmathematics;newresultsincludethestudyoftheexistenceofattractorsforalargenumberofsystemsinmathematicalphysicsandmechanics;lowerandupperestimatesonthedimensionoftheattractors;approximationofattractors;inertialmanifoldsandtheirapproximation.Thestudyofmultilevelnumericalmethodsstemmingfromdynamicalsystemstheoryhasalsodevelopedasasubjectonitsown.Finally，intermediateconceptsbetweenattractorsandinertialmanifoldshavealsobeenintroduced，inparticulartheconceptofinertialsets.
本书为英文版。
-
目录:
PrefacetotheSecondEdition
PrefacetotheFirstEdition
GENERALINTRODUCTION.
TheUser‘sGuide
Introduction
1.MechanismandDescriptionofChaos.TheFinite-DimensionalCase
2.MechanismandDescriptionofChaos.TheInfinite-DimensionalCase
3.TheGlobalAttractor.ReductiontoFiniteDimension
4.RemarksontheComputationalAspect
5.TheUser‘sGuide
CHAPTERⅠGeneralResultsandConceptsonInvariantSetsandAttractors
Introduction
1.Semigroups，InvariantSets，andAttractors
2.ExamplesinOrdinaryDifferentialEquations
3.FractalInterpolationandAttractors
CHAPTERⅡElementsofFunctionalAnalysis
Introduction
1.FunctionSpaces
2.LinearOperators
3.LinearEvolutionEquationsoftheFirstOrderinTime
4.LinearEvolutionEquationsoftheSecondOrderinTime
CHAPTERⅢAttractorsoftheDissipativeEvolutionEquationoftheFirstOrderinTime:Reaction-DiffusionEquations.FluidMechanicsandPatternFormationEquationsIntroduction
1.Reaction-DiffusionEquations
2.Navier-StokesEquations（n=2）
3.OtherEquationsinFluidMechanics
4.SomePatternFormationEquations
5.SemilinearEquations
6.BackwardUniqueness
CHAPTERⅣAttractorsofDissipativeWaveEquations
Introduction
1.LinearEquations:SummaryandAdditionalResults
2.TheSine-GordonEquation
3.ANonlinearWaveEquationofRelativisticQuantumMechanics
4.AnAbstractWaveEquation
5.TheGinzburg-LandauEquation
6.WeaklyDissipativeEquations.I.TheNonlinearSchr6dingerEquation
7.WeaklyDissipativeEquationsII.TheKorteweg-DeVriesEquation
8.UnboundedCase:TheLackofCompactness
9.RegularityofAttractors
10.StabilityofAttractors
CHAPTERⅤLyapunovExponentsandDimensionofAttractors
Introduction
1.LinearandMultilinearAlgebra
2.LyapunovExponentsandLyapunovNumbers
3.HausdorffandFractalDimensionsofAttractors
CHAPTERⅥExplicitBoundsontheNumberofDegreesofFreedomandtheDimensionofAttractorsofSomePhysicalSystems
Introduction
1.TheLorenzAttractor
2.Reaction-DiffusionEquations
3.Navier-StokesEquations（n=2）
4.OtherEquationsinFluidMechanic
5.PatternFormationEquations
6.DissipativeWaveEquations
7.TheGinzburg-LandauEquation
8.DifferentiabilityoftheSemigroup
CHAPTER ⅦNon-Well-PosedProblems,UnstableManifolds,LyapunovFunctions,andLowerBoundsonDimensions
Introduction
PARTA:NoN-WELL-POSEDPROBLEMS
1.DissipativityandWellPosedness
2.EstimateofDimensionforNon-Well-PosedProblems:ExamplesinFluidDynamics
PARTB:UNSTABLEMANIFOLDS,LYAPUNOVFUNCTIONS,ANDLOWERBOUNDSONDIMENSIONS
3.StableandUnstableManifolds
4.TheAttractorofaSemigroupwithaLyapunovFunction
5.LowerBoundsonDimensionsofAttractors:AnExample
CHAPTERⅧTheConeandSqueezingProperties.InertialManifolds
Introduction
1.TheConeProperty
2.ConstructionofanInertialManifold:DeScriptionoftheMethod
3.ExistenceofanInertialManifold
4.Examples
5.ApproximationandStabilityoftheInertialManifoldwithRespecttoPerturbations
CHAPTERⅨInertialManifoldsandSlowManifolds.TheNon-Self-AdjointCase
Introduction
1.TheFunctionalSetting
2.TheMainResultLipschitzCase
3.ComplementsandApplications
4.InertialManifoldsandSlowManifolds
CHAPTERⅩApproximationofAttractorsandInertialManifolds.ConvergentFamiliesofApproximateInertialManifolds
Introduction
1.ConstructionoftheManifolds
2.ApproximationofAttractors
3.ConvergentFamiliesofApproximateInertialManifolds
APPENDIXCollectiveSobolevInequalities
Introduction
1.NotationsandHypotheses
2.SpectralEstimatesforSchrodinger-TypeOperators
3.GeneralizationoftheSobolev-Lieb-ThirringInequalityⅠ
4.GeneralizationoftheSobolev-Lieb-ThirringInequalityⅡ
5.Examples
Bibliography
Index
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