偏微分方程

(德) 约翰 (John,F.) , 著

出版社：世界图书出版公司北京公司

年代：2009

定价：35.0

书籍简介:

本书是一部非常优秀的介绍偏微分方程的入门书，可以作为研究生阶段学习的基石。本书详尽的介绍了偏微分方程理论的重要方面，并从数学分析的角度做了进一步的探讨。本书是第4版，增加了全新的一章讲述无解线性方程的Lewy例子。

书籍目录:

Chapter1TheSingleFirst-OrderEquation

1.Introduction

2.Examples

3.AnalyticSolutionandApproximationMethodsinaSimpleExample

Problems

4.Quasi-linearEquations

5.TheCauchyProblemfortheQuasi-linearEquation

6.Examples

Problems

7.TheGeneralFirst-OrderEquationforaFunctionofTwoVariables

8.TheCauchyProblem

9.SolutionsGeneratedasEnvelopes

Problems

Chapter2Second-OrderEquations:HyperbolicEquationsforFunctionsofTwoIndependentVariables

1.CharacteristicsforLinearandQuasi-linearSecond-orderEquations

2.PropagationofSingularities

3.TheLinearSecond-OrderEquation

Problems

4.TheOne-DimensionalWaveEquation

Problems

5.SystemsofFirst-OrderEquations

6.AQuasi-linearSystemandSimpleWaves

Problem

Chapter3CharacteristicManifoldsandtheCauchyProblem

1.NotationofLaurentSchwartz

Problems

2.TheCauchyProblem

Problems

3.RealAnalyticFunctionsandtheCauchy-KowalevskiTheorem

(a)Multipleinfiniteseries

Problems

(b)Realanalyticfunctions

Problems

(c)Analyticandrealanalyticfunctions

Problems

(d)TheproofoftheCauchy-Kowalevskitheorem

Problems

4.TheLagrange-GreenIdentity

5.TheUniquenessTheoremofHolmgren

Problems

6.DistributionSolutions

Problems

Chapter4TheLaplaceEquation

1.GreensIdentity.FundamentalSolutions,andPoissonsEquation

Problems

2.TheMaximumPrinciple

Problems

3.TheDirichletProblem,GreensFunction,andPoissonsFormula

Problems

4.ProofofExistenceofSolutionsfortheDirichletProblemUsingSubharmonicFunctions("PerronsMethod")

Problems

5.SolutionoftheDirichletProblembyHilbert-SpaceMethods

Problems

Chapter5HyperbolicEquationsinHigherDimensions

1.TheWaveEquationinn-DimensionalSpace

(a)Themethodofsphericalmeans

Problems

(b)Hadamardsmethodofdescent

Problems

(c)DuhamelsprincipleandthegeneralCauchyproblem

Problem

(d)Initial-boundary-valueproblems("Mixed"problems)

Problems

2.Higher-OrderHyperbolicEquationswithConstantCoefficients

(a)Standardformoftheinitial-valueproblem

Problem

(b)SolutionbyFouriertransformation

Problems

(c)SolutionofamixedproblembyFouriertransformation

(d)Themethodofplanewaves

Problems

3.SymmetricHyperbolicSystems

(a)Thebasicenergyinequality

Problems

(b)Existenceofsolutionsbythemethodoffinitedifferences

Problems

(c)Existenceofsolutionsbythemethodofapproximationbyanalyticfunctions(MethodofSchauder)

Chapter6Higher-OrderEllipticEquationswithConstantCoefficients

1.TheFundamentalSolutionforOddn

Problems

2.TheDirichletProblem

Problems

3.MoreontheHilbertSpaceH~andtheAssumptionofBoundaryValuesintheDirichletProblem

Problems

Chapter7

ParabolicEquations

1.TheHeatEquation

(a)Theinitial-valueproblem

Problems

(b)Maximumprinciple,uniqueness,andregularity

Problem

(c)Amixedproblem

Problems

(d)Non-negativesolutions

Problems

2.TheInitial-ValueProblemforGeneralSecond-OrderLinear

ParabolicEquations

(a)Themethodoffinitedifferencesandthemaximumprinciple

(b)Existenceofsolutionsoftheinitial-valueproblem

Problems

H.LewysExampleofaLinearEquationwithoutSolutions

Problems

Bibliography

Glossary

Index

内容摘要:

　　Aconsiderableamountofnewmaterialhasbeenaddedtothisedition.ThereisanextensivediscussionofrealanalyticfunctionsofseveralvariablesinChapter3.ThispermitsestimationofthesizeofthedomainofexistenceintheCauchy-Kowalevskitheorem.AfirstapplicationoftheseestimatesconsistsinarigorousproofofanewversionofHolmgrensuniquenesstheoremforlinearanalyticpartialdifferentialequations(onlysketchedintheearliereditions).

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出版地	北京	出版单位	世界图书出版公司北京公司
版次	4版	印次	1
定价(元)	35.0	语种	英文
尺寸	14	装帧	平装
页数		印数	1000

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书籍信息归属:

偏微分方程是世界图书出版公司北京公司于2009.05出版的中图分类号为 O175.2 的主题关于偏微分方程－英文的书籍。