稀薄气体的数学理论（影印版）

图书标准信息

• 作者 [意]切尔奇纳尼 著
• 出版社 高等教育出版社
• 出版时间 2009-02
• 版次 1
• ISBN 9787040255355
• 定价 28.40元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 317页
• 字数 430千字
• 正文语种 英语
• 丛书 天元基金影印数学丛书

【内容简介】

《稀薄气体的数学理论（影印版）》讲述了稀薄气体的数学理论（Boltzmann方程的数学理论）中的三个主要问题直到1994年的理论发展，包括BoItzmann方程是怎样从经典力学推出来的，即BoItzmann方程是怎样从Liouville方程推出来的；Boltzmann方程解的存在性和唯一性问题；Boltzmann方程与流体力学的关系，即EuIer方程和Navier-Stokes方程是怎样从Liouville方程推出来的。另外，《稀薄气体的数学理论（影印版）》还介绍了O．LanfordⅢ，DiPerna，P．L.Lions等的出色工作，可作为BOItzmann方程的数学理论的优秀的教材和参考书。

【目录】

Introduction
1HistoricalIntroduction
1.1WhatisaGas?FromtheBilliardTabletoBoylesLaw
1.2BriefHistoryofKineticTheory
2InformalDerivationoftheBoltzmannEquation
2.1ThePhaseSpaceandtheLiouvilleEquation
2.2BoltzmannsArgumentinaModernPerspective
2.3MolecularChaos.CritiqueandJustification
2.4TheBBGKYHierarchy
2.5TheBoltzmannHierarchyandItsRelationtotheBoltzmannEquation
3ElementaryPropertiesoftheSolutions
3.1CollisionInvariants33
3.2TheBoltzmannInequalityandtheMaxwellDistributions
3.3TheMacroscopicBalanceEquations
3.4TheH-Theorem
3.5LoschmidtsParadox
3.6PoincaresRecurrenceandZermelosParadox
3.7EquilibriumStatesandMaxwellianDistributions
3.8HydrodynamicalLimitandOtherScalings
4RigorousValidityoftheBoltzmannEquation
4.1SignificanceoftheProblem
4.2Hard-SphereDynamics
4.3TransitiontoL1.TheLiouvilleEquationandtheBBGKYHierarchyRevisited
4.4RigorousValidityoftheBoltzmannEquation
4.5ValidityoftheBoltzmannEquationforaRareCloudofGasintheVacuum
4.6Interpretation
4.7TheEmergenceofIrreversibility
4.8MoreontheBoltzmannHierarchy
Appendix4.AMoreaboutHard-SphereDynamics
Appendix4.BARigorousDerivationoftheBBGKYHierarchy
Appendix4.CUchiyamasExample
5ExistenceandUniquenessResults
5.1PreliminaryRemarks
5.2ExistencefromValidity,andOverview
5.3AGeneralGlobalExistenceResult
5.4GeneralizationsandOtherRemarks
Appendix5.A
6TheInitialValueProblemfortheHomogeneousBoltzmannEquation
6.1AnExistenceTheoremforaModifiedEquation
6.2RemovingtheCutoff：TheL1-TheoryfortheFullEquation
6.3TheL∞-TheoryandClassicalSolutions
6.4LongTimeBehavior
6.5FurtherDevelopmentsandComments
Appendix6.A
Appendix6.B
Appendix6.C
7PerturbationsofEquilibriaandSpaceHomogeneousSolutions
7.1TheLinearizedCollisionOperator
7.2TheBasicPropertiesoftheLinearizedCollisionOperator
7.3SpectralPropertiesoftheFourier-Transformed,LinearizedBoltzmannEquation
7.4TheAsymptoticBehavioroftheSolutionoftheCauchyProblemfortheLinearizedBoltzmannEquation
7.5TheGlobalExistenceTheoremfortheNonlinearEquation
7.6Extensions：ThePeriodicCaseandProblemsinOneandTwoDimensions
7.7AFurtherExtension：SolutionsClosetoaSpaceHomogeneousSolution
8BoundaryConditions
8.1Introduction
8.2TheScatteringKernel
8.3TheAccommodationCoefficients
8.4MathematicalModels
8.5ARemarkableInequality
9ExistenceResultsforInitial-BoundaryandBoundaryValueProblems
9.1PreliminaryRemarks
9.2ResultsontheTraces
9.3PropertiesoftheFree-StreamingOperator
9.4ExistenceinaVesselwithIsothermalBoundary
9.5RigorousProofoftheApproachtoEquilibrium
9.6PerturbationsofEquilibria
9.7ASteadyProblem
9.8StabilityoftheSteadyFlowPastanObstacle
9.9ConcludingRemarks
10ParticleSimulationoftheBoltzmannEquation
10.1RationaleamdOverview
10.2LowDiscrepancyMethods
10.3BirdsScheme
11HydrodynamicalLimits
11.1AFormalDiscussion
11.2TheHilbertExpansion
11.3TheEntropyApproachtotheHydrodynamicalLimit
11.4TheHydrodynamicalLimitforShortTimes
11.5OtherScalingsandtheIncompressibleNavier-StokesEquations
12OpenProblemsandNewDirections
AuthorIndex
SubjectIndex