非自伴且主算子不可逆的抽象边值问题

@吴开谡 $中国原子能科学研究院核物理研究所!北京102413@叶建军$ 西南交通大学数学系!四川成都610031@阳名珠$中国原子能科学研究院核物理研究所!北京102413

详细信息

Non-self-adjoint Abstract Boundary Value Problem With Non invertible Main Operator

摘要: 在Hibert空间H中研究了一类非自伴且主算子不可逆的抽象边值问题, 利用空间分解的技巧, 证明了抽象边值问题解的适定性
- 抽象边值问题 ,
- 空间分解 ,
- λ线性流形
Abstract: boundary value problem whose main operator is non invertible is studied. Using technique of decomposition space, it is proved that the abstract boundary problem is well pose.
- abstract boundary value problem ,
- decomposition space ,
- λ linear mainfold

[1]	BealsR. AnAbstractTreatmentofSomeForward backwardProblemsofTransportandScattering[J]. Jour nalofFunctionalAnalysis,1979,34:1～20.
[2]	vanderMeeCVM. KineticEquationWithCollisionOperatorofSpectralRadiusLessThanOne[J]. Trans portTheoryandStatisticalPhysics,1978,17(1):147～160.
[3]	GreenbergW, vanderMeeCVM, ProtopopescuV. BoundaryValueProblemsinAbstractKineticTheory[M]. Boston:BaselandBostonBirkha櫣ｓｅｒＯＴ,1987.23.
[4]	LekerkerkerCG. TheLinearTransportEquation;TheDegenerateCasec=1[J]. ProcRoyalSocEdin burgh,1975/76,75A :259～282;283～295.
[5]	HangelbrokeRJ. OntheDispersionFunctionofTransportTheory[J]. TransportTheoryandStatisticalPhysics,1979,18(3):133～146.
[6]	ZweifielPF. TwentyYearsofTransportTheory[J]. TransportTheoryandStatisticalPhysics,1978,17(1):139～146.
[7]	许跟起.抽象动力方程的适定性[J]. 数学物理学报,1992,12(1):56～67.
[8]	GreenbergW, vanderMeeCVM, WalusW. StrongSolutionsofStationaryEquationsinAbstractKineticTheory[J]. IntegralEquationsandOperatorTheory,1988,11:186～204.