激波和反应扩散方程影印版（第2版）

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作　者：	Joel Smoller
出版社：	北京世图
丛编项：	A Series of Comprehensive Studies in Mathematics
标　签：	暂缺

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ISBN：	9787506241007	出版时间：	2004-06-01	包装：	出版日期：1999-3-1 版次：1版1次
开本：	32开	页数：	632	字数：

内容简介

　　My main purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for its applications in modern analysis. If I have accomplished my purpose， then the book should be found usable both as a text for students and as a source of reference for the more advanced mathematician. I have tried to keep to a minimum the amount of new and unusual terminology and notation. In the few places where my nomenclature differs from that in the existing literature of measure theory， I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are， for instance， sound algebraic reasons for using the terms "lattice" and "ring" for certain classes of sets：reasons which are more cogent than the similarities that caused Hausdorff to use "ring" and "field."本书为英文版。

作者简介

暂缺《激波和反应扩散方程影印版（第2版）》作者简介

图书目录

Acknowledgment
PrefacetotheSecondEdition
PrefacetotheFirstEdition
ListofFrequentlyUsedSymbols
PARTI
BasicLinearTheory
CHAPTER1
Ill-PosedProblems
A.SomeExamples
B.Lewy'sExample
CHAPTER2
CharacteristicsandInitial-ValueProblems
CHAPTER3
TheOne-DimensionalWaveEquation
CHAPTER4
UniquenessandEnergyIntegrals
CHAPTER5
Holmgren'sUniquenessTheorem
CHAPTER6
AnInitial-ValueProblemforaHyperbolicEquation
CHAPTER7
DistributionTheory
A.ACursoryView
B.FundamentalSolutions
C.Appendix
CHAPTER8
Second-OrderLinearEllipticEquations
A.TheStrongMaximumPrinciple
B.A-PrioriEstimates
C.ExistenceofSolutions
D.EllipticRegularity
CHAPTER9
Second-OrderLinearParabolicEquations
A.TheHeatEquation
B.StrongMaximumPrinciples
PARTII
Reaction-DiffusionEquations
CHAPTER10
ComparisonTheoremsandMonotonicityMethods
A.ComparisonTheoremsforNonlinearEquations
B.UpperandLowerSolutions
C.Applications
CHAPTER11
Linearization
A.SpectralTheoryforSelf-AdjointOperators
B.LinearizedStability
C.Appendix:TheKrein-RutmanTheorem
CHAPTER12
TopologicalMethods
A.DegreeTheoryinRn
B.TheLeray-SchauderDegree
C.AnIntroductiontoMorseTheory
D.ARapidCourseinTopology
CHAPTER13
BifurcationTheory
A.TheImplicitFunctionTheorem
B.StabilityofBifurcatingSolutions
C.SomeGeneralBifurcationTheorems
D.SpontaneousBifurcation;AnExample
CHAPTER14
SystemsofReaction-DiffusionEquations
A.LocalExistenceofSolutions
B.InvariantRegions
C.AComparisonTheorem
D.DecaytoSpatiallyHomogeneousSolutions
E.ALyapunovFunctionforContractingRectangles
F.ApplicationstotheEquationsofMathematicalEcology
PARTIII
TheTheoryofShockWaves
CHAPTER15
DiscontinuousSolutionsofConservationLaws
A.DiscontinuousSolutions
B.WeakSolutionsofConservationLaws
C.EvolutionarySystems
D.TheShockInequalities
E.Irreversibility
CHAPTER16
TheSingleConservationLaw
A.ExistenceofanEntropySolution
B.UniquenessoftheEntropySolution
C.AsymptoticBehavioroftheEntropySolution
D.TheRiemannProblemforaScalarConservationLaw
CHAPTER17
TheRiemannProblemforSystemsofConservationLaws
A.Thep-System
B.ShocksandSimpleWaves
C.SolutionoftheGeneralRiemannProblem
CHAPTER18
ApplicationstoGasDynamics
A.TheShockInequalities
B.TheRiemannProbleminGasDynamics
C.InteractionofShockWaves
CHAPTER19
TheGlimmDifferenceScheme
A.TheInteractionEstimate
B.TheDifferenceApproximation
C.Convergence
CHAPTER20
RiemannInvariants,Entropy,andUniqueness
A.Riemannlnvariants
B.AConceptofEntropy
C.Solutionswith"Big"Data
D.InstabilityofRarefactionShocks
E.Oleinik'sUniquenessTheorem
CHAPTER21
Quasi-LinearParabolicSystems
A.GradientSystems
B.ArtificialViscosity
C.IsentropicGasDynamics
PARTIV
TheConleyIndex
CHAPTER22
TheConleyIndex
A.AnImpressionisticOverview
B.IsolatedInvariantSetsandIsolatingBlocks
C.TheHomotopyIndex
CHAPTER23
IndexPairsandtheContinuationTheorem
A.MorseDecompositionsandIndexPairs
B.TheConleyIndexofanIsolatedInvariantSet
C.Continuation
D.SomeFurtherRemarks
CHAPTER24
TravellingWaves
A.TheStructureofWeakShockWaves
B.TheStructureofMagnetohydrodynamicShockWaves
C.PeriodicTravellingWaves
D.StabilityorSteady-StateSolutions
E.InstabilityofEquilibriumSolutionsortheNeumannProblem
F.Appendix:ACriterionforNondegeneracy
CHAPTER25
RecentResults
SectionI.Reaction-DiffusionEquations
A.StabilityoftheFitz-Hugh-NagumoTravellingPulse
B.Symmetry-Breaking
C.ABifurcationTheorem
D.EquivariantConleyIndex
E.ApplicationtoSemilinearEllipticEquations
ConcludingRemarks
SectionII.TheoryofShockWaves
A.CompensatedCompactness
B.StabilityofShockWaves
C.MiscellaneousResults
SectionIII.ConleyIndexTheory
A.TheConnectionIndex
B.Conley'sConnectionMatrix
C.MiscellaneousResults
SectionIV.StabilityofTravellingWaves--ATopologicalApproach
A.Introduction
B.TheSearchforp(L)
C.ApplicationstoFast-SlowSystems
References
Bibliography
AuthorIndex
SubjectIndex