种群细胞中迁移半群本质谱的稳定性

Stability of the Essential Spectrum for Transport Semigroup in Growing Cell Populations

在Lp(1<p<+∞)空间上,研究了一类具光滑边界条件的L-R型迁移方程,利用所谓的预解方法和半群方法证明了这类模型相应的迁移半群的Dyson-Phillips展开式的一阶余项R1(t)的紧性和迁移半群本质谱的稳定性,从而获得了该迁移算子的谱性质及迁移方程解的渐近稳定性等结果.

We discuss the L-R model with smooth boundary conditions in Lp(1<p<+∞) space,We prove that the first-order remainder term R1(t)of the Dyson-Phillips expansion of the transport semigroup for this model is compact and the stability of the essential spectrum by so-called resolvent approach and the semigroup approach.In the last,we get the spectrum of the transport operator and the stability of the solution to the transport equation and so on.