郭柏灵论文集

1998年

PartialRegularityforTwoDimensionalLandau-LifshitzEquations

GlobalAttractorofaClassofStronglyDampedNonlinearWaveEquations

耦合Schrodinger-KdV方程组Cauchy问题的适定性

SlowTime-periodicSolutionsofCubic-quinticGinzburg-LandauEquation(I)

--EquilibriaProblem

SlowTime-periodicSolutionsofCubic-quinticGinzburg-LandauEquation(II)

--HeteroclinicOrbits

AttractorsfortheLong-shortWaveEquations

Initial-boundaryValueProblemfortheLandau-LifshitzSystem(I)

--ExistenceandPartialRegularity

Initial-boundaryValueProblemfortheLandau-LifshitzSystem(II)

--Uniqueness

GevreyClassRegularityandApproximateInertialManifoldsfortheNewton-BoussinesqEquations

AttractorfortheDissipativeGeneralizedKlein-Gordon-SchrodingerEquations

TheGlobalSmoothSolutionforLandau-Lifshitz-MaxwellEquationwithoutDissipation

GlobalAttractorandItsDimensionEstimatesfortheGeneralizedDissipativeKdVEquationonR

AttractorfortheDissipativeHamiltonianAmplitudeEquationGoverningModulatedWaveInstabilities

LongTimeBehaviorofStronglyDampedNonlinearWaveEquations

Space-timeMeansandSolutionstoaClassofNonlinearParabolicEquations

OrbitalStabilityofSolitaryWavesoftheLongWave-shortWaveResonanceEquations

Well-posednessofCauchyProblemforCoupledSystemofLong-shortWaveEquations

GlobalFlowGeneratedbyCoupledSystemofSchrodinger-BBMEquations

RemarksontheGlobalAttractorsofSemigroupsHavingaLyapunovFunctional

ApproximateInertialManifoldsofNon-NewtonianViscousIncompressibleFluids

1999年

LongTimeBehaviorofNonlinearStrainWavesinElasticWaveguides

SmoothSolutionforOne-dimensionalInhomogeneousHeisenbergChainEquations

SmoothSolutionoftheGeneralizedSystemofFerromagneticChain

Well-posednessoftheCauchyProblemfortheCoupledSystemoftheSchrodinger-KdVEquations

TheCauchyProblemforDavey-StewartsonSystems

SolitaryWavesforTwo-dimensionalSchr6dinger-Kadomtsev-PetviashviliEquations

GlobalExistenceofSmoothSolutiontoNonlinearThermoviscoelasticSystemwithClampedBoundaryConditionsinSolid-likeMaterials

AsymptoticBehavioroftheSolutiontotheSystemforaViscousReactiveGas

Long-timeUniformStabilityofSolutiontoMagnetohydrodynamicsEquation

Measure-valuedSolutiontotheStronglyDegenerateCompressibleHeisenbergChainEquations

OrbitalStabilityofSolitaryWavesofCoupledKdVEquations

2000年

三维Wigner-Poisson方程组的Cauchy问题

TheAttractorsforLandau-Lifshitz-MaxwellEquations

GlobalAttractorofNonlinearStrainWavesinElasticWaveguides

Initial-boundaryValueProblemfortheUnsaturatedLandau-LifshitzSystem

ExponentialAttractorsfortheGeneralizedGinzburg-LandauEquation

GlobalExistenceofSolutionstotheDerivative2DGinzburg-LandauEquation

ApproximateInertialManifoldsforDavey-StewartsonEquations

OntheWeakSolutiontotheEquationsofAntiferromagnets

ExistenceandBlow-upofSolutionstoDegenerateDavey-StewartsonEquations

Initial-boundaryValueProblemfortheLandau-LifshitzSystemwithAppliedField

AlgebraicL2DecayfortheSolutiontoaClassSystemofNon-NewtonianFluidinR

AttractorsfortheGinzburg-Landau-BBMEquationsinanUnboundedDomain

2001年

具调和振子的非线性Schrodinger方程

LongTimeBehaviorofSolutionsofDavey-StewartsonEquations

NeumannProblemfortheLandau-Lifshitz-MaxwellSysteminTwoDimensions

SomeExactNontrivialGlobalSolutionswithValuesinUnitSphereforTwo-dimensionalLandau-LifshitzEquations

ExistenceofthePeriodicSolutionfortheWeaklyDampedSchrodinger-BoussinesqEquation

AlmostPeriodicSolutionofGeneralizedGinzburg-LandauEquation

OntheInitialValueProblemandScatteringofSolutionsfortheGeneralizedDavey-StewartsonSystems

三维Wigner-Poisson方程解的渐进性

TheGlobalSolutionforLandau-Lifshitz-MaxwellEquations

Time-periodicSolutionstotheGinzburg-Landau-BBMEquations

具非均匀介电常数的半导体方程组的初边值问题

后记

　　郭柏灵院士三十多年来，潜心于非线性发展方程的理论研究，其中包括Landau-Lifshitz方程、Benjamin-one方程等，很多该类型的非线性发展方程都具有明显的实际背景，而且都有鲜明的特性，如强非线性耦合性和奇异性等。研究了这些方程大初值可解性、解的惟一性、正则性、渐近行为以及爆破现象等，完善了数学理论。　　这套《郭柏灵论文集》按照郭老师在不同时期所从事的研究领域，分成多卷出版。文集中所搜集的都是郭老师正式发表过的学术成果。把这些成果整理成集出版，不仅系统地反映了他的科研成就，更重要的是对于从事这方面学习、研究的学者无疑大有裨益。本书为《郭柏灵论文集》的第五卷。