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激波和反应扩散方程 第2版 英文版 Joel Smoller 著 1999年版
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激波和反应扩散方程 第2版 英文版
作者：Joel Smoller 著
出版时间：1999年版
内容简介:
Mymainpurposeinthisbookistopresentaunifiedtreatmentofthatpartofmeasuretheorywhichinrecentyearshasshownitselftobemostusefulforitsapplicationsinmodernanalysis.IfIhaveaccomplishedmypurpose,thenthebookshouldbefoundusablebothasatextforstudentsandasasourceofreferenceforthemoreadvancedmathematician.
Ihavetriedtokeeptoaminimumtheamountofnewandunusualterminologyandnotation.Inthefewplaceswheremynomenclaturediffersfromthatintheexistingliteratureofmeasuretheory,Iwasmotivatedbyanattempttoharmonizewiththeusageofotherpartsofmathematics.Thereare,forinstance,soundalgebraicreasonsforusingtheterms"lattice"and"ring"forcertainclassesofsets--reasonswhicharemorecogentthanthesimilaritiesthatcausedHausdorfftouse"ring"and"field."
目录:
Acknowledgment
PrefacetotheSecondEdition
PrefacetotheFirstEdition
ListofFrequentlyUsedSymbols
PARTⅠBasicLinearTheory
CHAPTER1lll-PosedProblems
CHAPTER2CharacteristicsandInitial-ValueProblems
CHAPTER3TheOne-DimensionalWaveEquation
CHAPTER4UniquenessandEnergyIntegrals
CHAPTER5Holmgren'sUniquenessTheorem
CHAPTER6AnInitial-ValueProblemforaHyperbolicEquation
CHAPTER7DistributionTheory
CHAPTER8Second-OrderLinearEllipticEquations
CHAPTER9Second-OrderLinearParabolicEquations
PARTⅡReaction-DiffusionEquations
CHAPTER10ComparisonTheoremsandMonotonicityMethods
CHAPTER11Linearization
CHAPTER12TopologicalMethods
CHAPTER13BifurcationTheory
CHAPTER14SystemsofReaction-DiffusionEquations
PARTⅢTheTheoryofShockWaves
CHAPTER15DiscontinuousSolutionsofConservationLaws
CHAPTER16TheSingleConservationLaw
CHAPTER17TheRiemannProblemforSystemsofConservationLaws
CHAPTER18ApplicationstoGasDynamics
CHAPTER19TheGlimmDifferenceScheme
CHAPTER20RiemannInvariants.Entropy.andUniqueness
CHAPTER21Quasi-LinearParabolicSystems
PARTⅣTheConleyIndex
CHAPTER22TheConleyIndex
CHAPTER23IndexPairsandtheContinuationTheorem
CHAPTER24TravellingWaves
CHAPTER25RecentResults
Bibliography
AuthorIndex
SubjectIndex
作者：Joel Smoller 著
出版时间：1999年版
内容简介:
Mymainpurposeinthisbookistopresentaunifiedtreatmentofthatpartofmeasuretheorywhichinrecentyearshasshownitselftobemostusefulforitsapplicationsinmodernanalysis.IfIhaveaccomplishedmypurpose,thenthebookshouldbefoundusablebothasatextforstudentsandasasourceofreferenceforthemoreadvancedmathematician.
Ihavetriedtokeeptoaminimumtheamountofnewandunusualterminologyandnotation.Inthefewplaceswheremynomenclaturediffersfromthatintheexistingliteratureofmeasuretheory,Iwasmotivatedbyanattempttoharmonizewiththeusageofotherpartsofmathematics.Thereare,forinstance,soundalgebraicreasonsforusingtheterms"lattice"and"ring"forcertainclassesofsets--reasonswhicharemorecogentthanthesimilaritiesthatcausedHausdorfftouse"ring"and"field."
目录:
Acknowledgment
PrefacetotheSecondEdition
PrefacetotheFirstEdition
ListofFrequentlyUsedSymbols
PARTⅠBasicLinearTheory
CHAPTER1lll-PosedProblems
CHAPTER2CharacteristicsandInitial-ValueProblems
CHAPTER3TheOne-DimensionalWaveEquation
CHAPTER4UniquenessandEnergyIntegrals
CHAPTER5Holmgren'sUniquenessTheorem
CHAPTER6AnInitial-ValueProblemforaHyperbolicEquation
CHAPTER7DistributionTheory
CHAPTER8Second-OrderLinearEllipticEquations
CHAPTER9Second-OrderLinearParabolicEquations
PARTⅡReaction-DiffusionEquations
CHAPTER10ComparisonTheoremsandMonotonicityMethods
CHAPTER11Linearization
CHAPTER12TopologicalMethods
CHAPTER13BifurcationTheory
CHAPTER14SystemsofReaction-DiffusionEquations
PARTⅢTheTheoryofShockWaves
CHAPTER15DiscontinuousSolutionsofConservationLaws
CHAPTER16TheSingleConservationLaw
CHAPTER17TheRiemannProblemforSystemsofConservationLaws
CHAPTER18ApplicationstoGasDynamics
CHAPTER19TheGlimmDifferenceScheme
CHAPTER20RiemannInvariants.Entropy.andUniqueness
CHAPTER21Quasi-LinearParabolicSystems
PARTⅣTheConleyIndex
CHAPTER22TheConleyIndex
CHAPTER23IndexPairsandtheContinuationTheorem
CHAPTER24TravellingWaves
CHAPTER25RecentResults
Bibliography
AuthorIndex
SubjectIndex
