具扰动项的L-R型迁移方程的谱问题

Spectral Problem of Transport Equation in L-R Model with Perturbation Term

本文在L_P(1≤p<+∞)空间上,研究了种群细胞增生中一类具扰动项的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<+∞)空间上是紧的,从而获得了该迁移算子的谱在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稳定性等结果.

The objective of this paper is to research the L-R model with perturbation term of cell populations in Lp（1≤P〈＋∞） space, it is to prove that the ninth-order remainder term Rg（t） of the Dyson-Phillips expansion of the transport operators generates semigroup for this model is weakly compact on L1 and is compact on （1〈P〈＋∞）, it is to obtain that the spectrum of the transport operators only consisting of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane and the stability of the transport equation solution and so on.