种群细胞增生中迁移半群的本质谱

Essential Spectrum of Transport Semigroup Arising in Growing Cell Populations

本文在L p(1<p<+∞)空间中,讨论了种群细胞增生中具部分光滑边界条件的迁移方算子A H生成的C0半群V(t)的Dyson-phillips展开式的第9阶余项R9(t)是紧算子,得到了该迁移群和streaming算子B H生成的C0半群U(t)有相同的本质谱半径.

In this paper, transport equation with partly smooth boundary conditions in cell populations is studied in space. It is to prove that the transport operator generates a senfigroup and the ninth - order remained term of the Dyson - phillips expansion of the semigroup is compact, and it is to obtain that the semigroup which is ger^erated by the transport operator and semigroup which is gen- erated by streaming operator have the same essential spectrum radius.