傅立叶分析和偏微分方程

图书标准信息

• 作者 R.Iorio、M.Iorio V.de 编
• 出版社 世界图书出版公司
• 出版时间 2003-09
• 版次 1
• ISBN 9787506265560
• 定价 78.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 411页

【内容简介】

ThisbookistheoutcomeofseveralcoursesandseminartalksheldattheInstitutodeMatematicaPuraeAplicada（IMPA）overtheyears.Itisagreatlymodifiedversionofapreviousworkbytheauthors,EquacoesDiferenciaisParciais,Umalntroducao,（ProjetoEuclides,IMPA,1978）.Ithasatwofoldpurpose,namelytointroducethestudenttothebasicconceptsofFourieranalysisandprovideillustrationsofrecentapplicationswheretheseconceptswereusedtostudyvariouspropertiesofthesolutionsofsomeimportantnonlinearevolutionequations.

【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
3.1CPeiodicFuncitons
3.2PerodicDistributions
3.3TopologicalRemakes
3.4FourierSeriesin
3.5TheConvolutionin
3.6SobolevSpaces

PartTwo:ApplicationstoPartialDfferentialEquations
4LinearEquations
5NonlinearEvolutionEquations
6TheKorteweg-deVriesEquation
7Distributions,FourierTransformandLinearEquations
8KdV,BOandFriends
AppendixAToolsfromtheTheoryofODEs
AppendixBCommutatorEstimates
Bibliography
Index