种群细胞增生中迁移算子的谱研究

The Spectral Research of Transport Operators Arising in Growing Cell Populations

在L_1空间上,利用线性算子理论探讨了种群细胞增生中一类具部分光滑边界条件的Rotenberg模型的迁移算子的谱,采用比较算子和豫解算子等方法证明了算子(λ-T_H)^(-1)κ的弱紧性以及算子丨Imλ|^(1/2)‖κ(λ-T_H)^(-1)κ‖(|Imλ|→+∞)在带域Γ_ω中的有界性,得到了该迁移算子A_H的谱在该带域中仅由有限个具有限代数重数的离散本征值组成.

In this paper, the spectrmn of the transport operators with partly smooth boundary conditions arising in growing cell populations is studied in L1 space. It is to prove that the operator（λ-TH）-1K is weakly compact and｜Imλ｜1/2K‖（λ-TH）-1K‖（｜Imλ｜→＋∞）is bounded in a trip Гω, and to obtain that the spectrum of the transport operator AH consist of finitely many isolate eigenvalues with a finite algebraic multiplicity in the trip. The main research methods rely on theory of linear operators, comparison operators and resolvent operators.