非线性复分析及其应用

闻国椿, 著

出版社：科学出版社

年代：2008

定价：82.0

书籍简介:

本书是一本数学专著，主要介绍作者们用复分析方法处理非线性一致椭圆型、抛物型、双曲型和混合（椭圆-双曲）型复方程及带抛物退化线的非线性椭圆型、双曲型和混合型复方程系统的研究成果。全书共分七章。第一至三章主要介绍一阶、二阶和四阶非线性椭圆型复方程与方程组解的性质和各种边值问题，其中也包含带抛物退化线的一阶和二阶非线性椭圆型复方程及间断Riemann-Hilbert边值问题与间断斜微商边值问题。第四章主要介绍二阶非线性（非散度型）抛物型复方程与方程组的一些边值问题，其中包括一种非正则初-斜微商边值问题。第五章主要介绍一阶和二阶非线性双曲型复方程的一些边值问题，而第六章主要介绍一阶和二阶带抛物退化线的非线性混合型复方程的一些边值问题，这种二阶混合型方程包含空气动力学中著名的Chaplygin方程作为特殊情况，而边值问题包括Tricomi问题，Frankl问题和斜微商问题等。第七章主要介绍上述理论和方法在非线性力学边值问题中的应用。

书籍目录:

Preface

Chapter1NonlinearEllipticComplexEquationsofFirstOrder

1.1DiscontinuousRiemann-HilbertProblemforNonlinearUniformly

EllipticComplexEquationsofFirstOrder

1.2BoundaryValueProblemsforEllipticComplexEquationswith

NonsmoothBoundary

1.3NonlinearRiemann-HilbertProblemforEllipticComplexEquations

inMultiplyConnectedDomains

1.4TheRiemann-HilbertProblemforQuasilinearDegenerateElliptic

ComplexEquationsofFirstOrder

1.5DiscontinuousRiemann-HilbertProblemforQuasilinearDegenerate

EllipticComplexEquationsofFirstOrder

Chapter2NonlinearEllipticEquationsofSecondOrder

2.1DiscontinuousObliqueDerivativeProblemforUniformlyElliptic

ComplexEquationsofSecondOrder

2.2PoincareBoundaryValueProblemforNonlinearEllipticEquationsof

SecondOrder

2.3GeneralObliqueDerivativeProblemforNonlinearEllipticEquations

ofSecondOrder

2.4DiscontinuousIrregularObliqueDerivativeProblemofNonlinear

EllipticEquationsofSecondOrder

2.5BoundaryValueProblemsforNonlinearDegenerateEllipticEquations

ofSecondOrder

Chapter3NonlinearEllipticSystemsofEquations

3.1BoundaryValueProblemsforUniformlyEllipticSystemsofSecond

OrderEquations

3.2BoundaryValueProblemsforNonlinearEllipticSystemsofSecond

OrderEquations

3.3BoundaryValueProblemsofNonlinearEllipticSystemsofSeveral

FirstOrderComplexEquations

3.4BoundaryValueProblemsforNonlinearEllipticSystemswith

SeveralUnknownFunctions

3.5DegenerateEllipticSystemsofSecondOrderwithSeveralUnknown

Functions

3.6BoundaryValueProblemsforNonlinearEllipticComplexEquations

SecondOrder

5.3ObliqueDerivativeProblemforQuasilinearDegenerateHyperbolic

EquationsofSecondOrder

5.4CauchyProblemforQuasilinearHyperbolicEquationswith

DegenerateRank0

5.5DarbouxTypeProblemforDegenerateHyperbolicSystemsof

SecondOrderEquations

Chapter6QuasilinearEquationsofMixedType

6.1TheRiemann-HilbertProblemforFirstOrderComplexEquationsof

MixedTypewithDegenerateLine

6.2TheTricomiProblemforSecondOrderQuasilinearEquationsof

MixedTypewithParabolicDegeneracy

6.3FranklTypeProblemforSecondOrderQuasilinearDegenerate

EquationsofMixedType

6.4BoundaryValueProblemsforDegenerateEquationsofMixedType

inMultiplyConnectedDomains

6.5ObliqueDerivativeProblemforQuasilinearEquationsofMixedType

withNonsmoothDegenerateLine

6.6ObliqueDerivativeProblemforSecondOrderQuasilinearSystems

ofMixedTypewithParabolicDegeneracy

Chapter7ApplicationsofNonlinearComplexAnalysistoContinuumMechanics

7.1FreeBoundaryProblemsinPlanarFiltration

7.2DegenerateEllipticBoundaryValueProblemandAxisymmetric

Filtration

7.3SomeFreeBoundaryProblemsinPlanarSubsonicFlow

7.4FreeBoundaryProblemsforCavityFlowsinGasDynamics

7.5FreeBoundaryProblemsinElastico-PlasticMechanics

References

内容摘要:

　　Thebookisacontinuationofdevelopmentof"Boundaryvalueproblemsfornonlinearellipticequationsandsystems"and"Linearandquasilinearequationsofhyperbolicandmixedtypes".Alargeportionoftheworkisdevotedtoboundaryvalueproblemsforgeneralellipticcomplexequationsoffirst,secondandfourthorder,initial-boundaryvalueproblemsfornonlinearparaboliccomplexequationsoffirstandsecondorder.Moreover,someresultsaboutfirstandsecondordercomplexequationsofmixed(elliptic-hyperbolic)typeareinvestigated.Applicationsofnonlinearcomplexanalysistocontinuummechanicsarealsointroduced.

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出版地	北京	出版单位	科学出版社
版次	1版	印次	1
定价(元)	82.0	语种	英文
尺寸	24	装帧	精装
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非线性复分析及其应用是科学出版社于2008.出版的中图分类号为 O174.5 ,O177.91 的主题关于非线性－复分析－英文的书籍。