一类具积分边界条件种群细胞迁移算子的本质谱

本文在L^1空间上，研究一类具积分边界条件种群细胞迁移方程，利用泛函分析中构造算子和比较算子方法及相关半群知识证明了迁移算子A_H产生的G_0半群V_H（t）的Dyson-Phillips展开式的n阶余项R_n（t）（n≥1）的弱紧性及V_H（t）和U_H（t）（streaming算子B_H产生）具有相同的本质谱及一致的本质谱型，得到了在区域Г中迁移算子A_H仅由有限个具有限代数重数的离散本征值组成及迁移方程解的渐近稳定性．

The Essential Spectral of Transport Operator in Growing Cell Population with Integral Boundary Conditions

This paper discusses the transport equations in growing cell population with integral boundary conditions in L_1-space. We prove that the weak compactness of the n-order remainder term R_n（t）（n ≥ 1） of the Dyson-Phillips expansion of C_0-semigroup VH （t） which generated by the operator AH and we also prove that the C_0-semigroup VH （t） and C_0-semigroup U_H （t） （generated by the streaming operator B_H） have the same essential spectral, the same type of the essential spectral by using the structuring operator, comparing operator and the knowledge of semigroup. In the last, we obtain that the spectrum of the transport operators A_H consists of finite isolate eigenvalues with finite algebraic multiplicity in trip F and the asymptotic stability of the solution of the transport equations.