一类非均匀介质迁移半群的本质谱  

The Essence Spectrum of A Transport Semigroup in Inhomogeneous Medium

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作  者:袁邓彬[1] YUAN Dengbin(School of Mathematics and Computational Science,Shangrao Normal,Shangrao Jiangxi 334001,China)

机构地区:[1]上饶师范学院数学与计算科学学院,江西上饶334001

出  处:《上饶师范学院学报》2024年第6期1-5,共5页Journal of Shangrao Normal University

基  金:江西省自然科学基金项目(20192BAB201004)。

摘  要:在L^(2)空间上,讨论了一类具非均匀介质、非连续能量和各向异性的迁移方程。首先,对迁移算子和扰动算子等多种算子进行构造;然后,应用半群理论证明这类迁移半群相应的一阶余项R_(1)(t)的紧性,从而得出该迁移算子A_(H)和B相应的半群V_(H)(t)和U(t)具有一致的本质谱型和相同的本质谱[σ_(ess)(V_(H)(t))=σ_(ess)(U(t))],能在不满足一定初值条件的情况下更精确地得出该迁移方程解的渐近行为;最后,证明了该迁移算子占优本征值的存在性。研究结果为进一步探讨迁移算子的谱型提供了一种新方法。In L^(2)space,the transport equations with inhomogeneous medium,anisotropic uncontinuous energy,and anisotropy were discussed.By constructing various operators such as transport operators and perturbation operators,and applying semigroup theory to prove the compactness of the remainder term R_(1)(t)about the corresponding transport semigroup,it could be concluded that transport semigroupV_(H)(t)and U(t)according to the operators A_(H)and B had the same type of the essence spectrum and the same essence spectrum[σ_(ess)(V_(H)(t))=σ_(ess)(U(t))].Therefore,the asymptotic behavior of the transport equation solution could be more accurately obtained without certain initial value conditions.Finally,the existence of the dominant eigenvalues of the transport operator was proved,providing a new method for further exploring the spectral types of transport operators.

关 键 词:本质谱 本质谱型 紧性 一致性 

分 类 号:O177.2[理学—数学]

 

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