本文選題：C0半群 + 擾動理論��； 參考：《鄭州大學(xué)》2015年碩士論文

【摘要】：在綜合運用泛函分析中的算子譜理論及C0半群的擾動理論等現(xiàn)代分析方法的前提下,本文對具各向異性、非均勻介質(zhì)的奇異中子遷移方程討論研究了其在?pL????p1空間上具廣義邊界條件下解的適定性和相關(guān)性質(zhì)。具體說來,本文把這類奇異遷移方程化成Lp空間抽象Cauchy問題,用C0算子半群理論找出解半群以證明該類方程解的適定性;然后根據(jù)Miyadera-Voigt擾動理論,給出該解半群的Dyson-Phillips展式的余項,利用測度卷積算子的方法證明了上述一階余項的緊性,因此得到該奇異遷移方程本質(zhì)譜的穩(wěn)定性,即擾動半群本質(zhì)譜的穩(wěn)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.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O177

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 陽名珠,朱廣田;具各向異性散射和裂變的中子遷移算子的譜[J];中國科學(xué);1981年01期

，

本文編號：1997968