书籍详情
傅立叶分析和偏微分方程
作者：约里奥（R.Iorio），约里奥（V.de M.Iorio）
出版社：世界图书出版公司北京公司
出版时间：2003-01-01
ISBN：9787506265560
定价：¥78.00
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内容简介
This book is the outcome of several courses and seminar talks held at the Instituto de Matematica Pura e Aplicada （IMPA） over the years.It is a greatly modified version of a previous work by the authors，Equacoes Diferenciais Parciais， Uma lntroducao， （Projeto Euclides， IMPA，1978）. It has a twofold purpose， namely to introduce the student to the basic concepts of Fourier analysis and provide illustrations of recent applications where these concepts were used to study various properties of the solutions of some important nonlinear evolution equations.本书为英文版。
作者简介
暂缺《傅立叶分析和偏微分方程》作者简介
目录
Preface
PartOne:FourierSeriesandPeriodicDistributions
1Preliminaries
1.1BasicDefinitionsandExamples
1.2ClassificationintoTypes
1.3Boundaryand/orInitialValueProblems
1.4SeparationofVariables:HeatFlowinaBar
1.5TheSchrodingerandtheWaveEquations
1.6TheDirichletProblemintheUnitCircle
1.7MaximumPrinciplesandUniqueness
2FourierSeries:BasicTheory
2.1SpacesofPeriodicFunctionsandSequences
2.2TheFourierTransform
2.3GeometricInterpretation
2.4DecayandDifferentiability
2.5TheInversionFormula:PointwiseConvergence
2.6PeriodicHeatFlow
2.7ApproximateIdentitiesandSummability
2.8CesaroSummability
3PeriodicDistributionsandSobolevSpaces
3.1CPeriodicFunctions
3.2PeriodicDistributions
3.3TopologicalRemarks
3.4FourierSeriesin
3.5TheConvolutionin
3.6SobolevSpaces
PartTwo:ApplicationstoPartialDifferentialEquations
4LinearEquations
4.1AFunctionalCalculus
4.2LinearEvolutionEquationsinHsper
4.3StronglyContinuousSemigroups*
4.4TheWaveEquation
5NonlinearEvolutionEquations
5.1LocalWell-PosednessRevisited
5.2MaximalIntervalsofExistence
5.3GNLSasaHamiltonianSystem
6TheKorteweg--deVriesEquation
6.1TheRegularizedProblem
6.2SomeFundamentalEstimates
6.3LocalWell-Posedness
6.4GlobalWell-Posedness
PartThree:SomeNonperiodieProblems
7Distributions,FourierTransformandLinearEquations
7.1Distributions
7.2TheFourierTransform
7.3Convolutions
7.4L2-typeSobolevSpacesinRn
7.5TheHeatand(Free)SchriSdingerEquations
8KdV,BOandFriends
8.1TheHs(R)Theory
8.2KdVinWeightedSobolevSpaces
8.3BOinWeightedSobolevSpaces
8.4Bore-likeInitialConditions
AppendixAToolsfromtheTheoryofODEs
AppendixBCommutatorEstimates
Bibliography
Index
PartOne:FourierSeriesandPeriodicDistributions
1Preliminaries
1.1BasicDefinitionsandExamples
1.2ClassificationintoTypes
1.3Boundaryand/orInitialValueProblems
1.4SeparationofVariables:HeatFlowinaBar
1.5TheSchrodingerandtheWaveEquations
1.6TheDirichletProblemintheUnitCircle
1.7MaximumPrinciplesandUniqueness
2FourierSeries:BasicTheory
2.1SpacesofPeriodicFunctionsandSequences
2.2TheFourierTransform
2.3GeometricInterpretation
2.4DecayandDifferentiability
2.5TheInversionFormula:PointwiseConvergence
2.6PeriodicHeatFlow
2.7ApproximateIdentitiesandSummability
2.8CesaroSummability
3PeriodicDistributionsandSobolevSpaces
3.1CPeriodicFunctions
3.2PeriodicDistributions
3.3TopologicalRemarks
3.4FourierSeriesin
3.5TheConvolutionin
3.6SobolevSpaces
PartTwo:ApplicationstoPartialDifferentialEquations
4LinearEquations
4.1AFunctionalCalculus
4.2LinearEvolutionEquationsinHsper
4.3StronglyContinuousSemigroups*
4.4TheWaveEquation
5NonlinearEvolutionEquations
5.1LocalWell-PosednessRevisited
5.2MaximalIntervalsofExistence
5.3GNLSasaHamiltonianSystem
6TheKorteweg--deVriesEquation
6.1TheRegularizedProblem
6.2SomeFundamentalEstimates
6.3LocalWell-Posedness
6.4GlobalWell-Posedness
PartThree:SomeNonperiodieProblems
7Distributions,FourierTransformandLinearEquations
7.1Distributions
7.2TheFourierTransform
7.3Convolutions
7.4L2-typeSobolevSpacesinRn
7.5TheHeatand(Free)SchriSdingerEquations
8KdV,BOandFriends
8.1TheHs(R)Theory
8.2KdVinWeightedSobolevSpaces
8.3BOinWeightedSobolevSpaces
8.4Bore-likeInitialConditions
AppendixAToolsfromtheTheoryofODEs
AppendixBCommutatorEstimates
Bibliography
Index
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