在$L_p(1\le p<+\mathrm{\infty })$空间上,研究了种群细胞增生中一类具扰动项非光滑边界条件的L-R模型,证明了这类模型相应的迁移算子生成半群的Dyson-phillips展式的9阶余项$R_9(t)$在$L_1$空间上是弱紧和在$L_p(1<p<+\mathrm{\infty })$空间上是紧的,从而获得了该迁移算子的谱在某右半平面上仅由有限个具有限代数重数的离散本征值组成及该迁移方程解的渐近行为等结果.

This paper deals with the L-R model with perturbation term of cell pop-ulations with unsmooth boundary conditions in Lp space (1 ≤ p < +∞). It is proven
that the ninth-order remainder term R9(t) of the Dyson-Phillips expansion of cor-responding transport operators generates semigroup for this model which is weakly compact on L1 and is compact on Lp(1 < p < +∞), and that the spectrum of the transport operators only consist of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane. Finally, the asymptotic behavior of the transport equation solution is given.