细菌种群模型中一类迁移算子的谱问题

Spectral Problem of a Transport Operator in Bacterial Population model

在L_1空间上研究了一般边界条件下一类具结构化的细菌种群模型,证明了这类模型相应的迁移算子生成半群的Dyson-phillips展式的余项R_9(t)是弱紧的,从而得到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等结果。

The objective of this paper is to research the model of structured bacterial population with generalize boundary conditions in L1 space,it is to prove that the remainder term R9（t）of the Dyson-Phillips expansion of corresponding transport operator generates semigroup for this model is weakly compact.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 so on.