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非线性抛物型方程在高维区域中的初:边值问题(英文影印版)
作者:Guochun Wen,Benteng Zou
出版社:Springer
出版时间:2006-06-01
ISBN:9787030091277
定价:¥76.00
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内容简介
This book deal with nonlinear parboic epuations and systems of second order in higher dimensional domains, aninly several initial-boundary value problems for nonlinear parabolic equations and systems of second order equatiohns with smooth coefficents or measurable coefficients are dixcussed. There are two characteristics of this booku. One is that parabolic equations are discussed in the nonilinear case and the boundary condittions include the irregualr oblique derivative case, another one is that boundary value problems are almost consicered in the case of multiply connected domains and several methotds anr used. This booku can be refered to the graduate students, researchers in partial differential equations and function theory at universites and institutes.
作者简介
暂缺《非线性抛物型方程在高维区域中的初:边值问题(英文影印版)》作者简介
目录
Preface
ChapterIPropertiesofSolutionsforParabolic
EquationsofSecondOrder
1.ConditionsofLinearandNonlinearParabolicEquationsofSecondOrder
2.ExtremumPrinciplesofSolutionsforParabolicEquationsofSecondOrder
3.UniquenessandStabilityofSolutionsforSomeInitial-BoundaryValueProblems
4.RepresentationTheoremandCompactnessPrincipleofSolutionsforParabolicEquations
5.Aleksandrov-Bakel'man-PucciTypeMaximumPrinciple
ChapterIINonlinearParabolicEquationsofSecond
OrderwithSmoothCoefficients
1.FormulationofInitial-IrregularObliqueDerivativeProblemforNonlinearParabolicEquationswithSmoothCoefficients
2.BoundednessandHhlderEstimatesofSolutionsofInitialRegularObliqueDerivativeProblemforEquation(1.2)
3.BoundednessandHhlderEstimatesofDerivativesofSolutionsofInitial-RegularObliqueDerivativeProblemforEquation(1.2)
4.APrioriEstimatesofDerivativesofSolutionsofInitial-IrregularObliqueDerivativeProblemforEquation(1.2)
5.SolvabilityoftheInitial-IrregularObliqueDerivativeProblemforEquation(1.2)
ChapterIIINonlinearParabolicEquationsofSecondOrderwithCordes(Measurable)Coefficients
1.FormulationofInitial-BoundaryValueProblemsforNonlinearParabolicEquations
2.InnerEstimatesofSolutionsofInitial-BoundaryValueProblemsforParabolicEquations
3.TheDirichletProblemandNuemannProblemforNonlinearParabolicEquations
4.Initial-ObliqueDerivativeProblemforNonlinearParabolicEquations
5.Initial-MixedBoundaryValueProblemsforNonlinearParabolicEquations
ChapterIVNonlinearParabolicSystemsofEquationswithCordes(Measurable)Coefficients
1.FormulationofInitial-ObliqueDerivativeProblemsforNonlinearParabolicSystems
2.SolvabilityofProblemDandProblemNforParabolicSystemsofSecondOrderEquations
3.Initial-ObliqueDerivativeBoundaryValueProblemforNonlinearParabolicSystems
4.Initial-MixedBoundaryValueProblemforNonlinearParabolicSystems
ChapterVLinearandQuasilinearParabolicEquationswithVMO(Measurable)Coefficients
1.SomeResultsofHarmonicAnalysisandFundamentalSolutionsofParabolicEquations
2.InteriorRepresentationandDirichletBoundaryValueProblemforLinearParabolicEquations
3.Initial-ObliqueDerivativeBoundaryValueProblemsforLinearParabolicEquations
4.QuasilinearParabolicEquationswithRegularBoundaryConditions
References
ChapterIPropertiesofSolutionsforParabolic
EquationsofSecondOrder
1.ConditionsofLinearandNonlinearParabolicEquationsofSecondOrder
2.ExtremumPrinciplesofSolutionsforParabolicEquationsofSecondOrder
3.UniquenessandStabilityofSolutionsforSomeInitial-BoundaryValueProblems
4.RepresentationTheoremandCompactnessPrincipleofSolutionsforParabolicEquations
5.Aleksandrov-Bakel'man-PucciTypeMaximumPrinciple
ChapterIINonlinearParabolicEquationsofSecond
OrderwithSmoothCoefficients
1.FormulationofInitial-IrregularObliqueDerivativeProblemforNonlinearParabolicEquationswithSmoothCoefficients
2.BoundednessandHhlderEstimatesofSolutionsofInitialRegularObliqueDerivativeProblemforEquation(1.2)
3.BoundednessandHhlderEstimatesofDerivativesofSolutionsofInitial-RegularObliqueDerivativeProblemforEquation(1.2)
4.APrioriEstimatesofDerivativesofSolutionsofInitial-IrregularObliqueDerivativeProblemforEquation(1.2)
5.SolvabilityoftheInitial-IrregularObliqueDerivativeProblemforEquation(1.2)
ChapterIIINonlinearParabolicEquationsofSecondOrderwithCordes(Measurable)Coefficients
1.FormulationofInitial-BoundaryValueProblemsforNonlinearParabolicEquations
2.InnerEstimatesofSolutionsofInitial-BoundaryValueProblemsforParabolicEquations
3.TheDirichletProblemandNuemannProblemforNonlinearParabolicEquations
4.Initial-ObliqueDerivativeProblemforNonlinearParabolicEquations
5.Initial-MixedBoundaryValueProblemsforNonlinearParabolicEquations
ChapterIVNonlinearParabolicSystemsofEquationswithCordes(Measurable)Coefficients
1.FormulationofInitial-ObliqueDerivativeProblemsforNonlinearParabolicSystems
2.SolvabilityofProblemDandProblemNforParabolicSystemsofSecondOrderEquations
3.Initial-ObliqueDerivativeBoundaryValueProblemforNonlinearParabolicSystems
4.Initial-MixedBoundaryValueProblemforNonlinearParabolicSystems
ChapterVLinearandQuasilinearParabolicEquationswithVMO(Measurable)Coefficients
1.SomeResultsofHarmonicAnalysisandFundamentalSolutionsofParabolicEquations
2.InteriorRepresentationandDirichletBoundaryValueProblemforLinearParabolicEquations
3.Initial-ObliqueDerivativeBoundaryValueProblemsforLinearParabolicEquations
4.QuasilinearParabolicEquationswithRegularBoundaryConditions
References
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