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偏微分方程(第4版)(英文版)
《偏微分方程(第4版)(英文版)》是一部非常优秀的介绍偏微分方程的入门书籍,可以作为研究生阶段学习的基石。《偏微分方程(第4版)(英文版)》详尽地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。《偏微分方程(第4版)(英文版)》是第4版,增加了全新的一章讲述无解线性方程的Lewy例子。
Chapter1 TheSingleFirst-OrderEquation1.Introduction2.Examples3.AnalyticSolutionandApproximationMethodsinaSimpleExampleProblems4.Quasi-linearEquations5.TheCauchyProblemfortheQuasi-linearEquation6.ExamplesProblems7.TheGeneralFirst-OrderEquationforaFunctionofTwoVariables8.TheCauchyProblem9.SolutionsGeneratedasEnvelopesProblemsChapter2 Second-OrderEquations:HyperbolicEquationsforFunctionsofTwoIndependentVariables1.CharacteristicsforLinearandQuasi-linearSecond-orderEquations2.PropagationofSingularities3.TheLinearSecond-OrderEquationProblems4.TheOne-DimensionalWaveEquationProblems5.SystemsofFirst-OrderEquations6.AQuasi-linearSystemandSimpleWavesProblemChapter3 CharacteristicManifoldsandtheCauchyProblem1.NotationofLaurentSchwartzProblems2.TheCauchyProblemProblems3.RealAnalyticFunctionsandtheCauchy-KowalevskiTheorem(a)MultipleinfiniteseriesProblems(b)RealanalyticfunctionsProblems(c)AnalyticandrealanalyticfunctionsProblems(d)TheproofoftheCauchy-KowalevskitheoremProblems4.TheLagrange-GreenIdentity5.TheUniquenessTheoremofHolmgrenProblems6.DistributionSolutionsProblemsChapter4 TheLaplaceEquation1.GreensIdentity.FundamentalSolutions,andPoissonsEquationProblems2.TheMaximumPrincipleProblems3.TheDirichletProblem,GreensFunction,andPoissonsFormulaProblems4.ProofofExistenceofSolutionsfortheDirichletProblemUsingSubharmonicFunctions("PerronsMethod")Problems5.SolutionoftheDirichletProblembyHilbert-SpaceMethodsProblemsChapter5 HyperbolicEquationsinHigherDimensions1.TheWaveEquationinn-DimensionalSpace(a)ThemethodofsphericalmeansProblems(b)Hadamardsmethodofdescent Problems……Chapter6 Higher-OrderEllipticEquationswithConstantChapter7ParabolicEquationsChapter8H.LewysExampleofaLinearEquationBibliographyGlossaryIndex
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