广义边界条件下奇异迁移方程本质谱的稳定性

发布时间：2018-06-09 00:36

本文选题：C0半群 + 扰动理论　；参考：《郑州大学》2015年硕士论文

【摘要】：在综合运用泛函分析中的算子谱理论及C0半群的扰动理论等现代分析方法的前提下,本文对具各向异性、非均匀介质的奇异中子迁移方程讨论研究了其在?pL????p1空间上具广义边界条件下解的适定性和相关性质。具体说来,本文把这类奇异迁移方程化成Lp空间抽象Cauchy问题,用C0算子半群理论找出解半群以证明该类方程解的适定性;然后根据Miyadera-Voigt扰动理论,给出该解半群的Dyson-Phillips展式的余项,利用测度卷积算子的方法证明了上述一阶余项的紧性,因此得到该奇异迁移方程本质谱的稳定性,即扰动半群本质谱的稳定性。
[Abstract]:On the premise of synthetically applying the theory of operator spectrum in functional analysis and the perturbation theory of C _ 0 semigroup, this paper has anisotropy. In this paper, we discuss the singular neutron transport equation of inhomogeneous medium. We study the fitness and correlation properties of the solution under the generalized boundary condition in the pLPl space. In this paper, the singular transfer equation is transformed into an abstract Cauchy problem in LP space, the solution semigroup is found by using the theory of C 0 operator semigroup to prove the fitness of the solution of the equation, and the remainder of the Dyson-Phillips expansion of the solution semigroup is given according to Miyadera-Voigt perturbation theory. The compactness of the first order coterm is proved by means of the measure convolution operator, so the stability of the mass spectrum of the singular migration equation is obtained, that is, the stability of the perturbation semigroup mass spectrometry.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177

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