一类具结构化的细菌种群模型中出现的迁移算子的谱分析

Spectral Analysis of a Transport Operator in Structured Bacterial Population

该文在L1空间上,研究了在总转变规则的边界条件下一类具结构化的细菌种群模型,讨论了该模型中出现的迁移算子的谱分析,证明了这类迁移算子生成的正不可约C0半群的弱紧性,得到了该迁移算子的谱仅由至多可数个具有限代数重数的离散本征值组成,且-∞是唯一可能的聚点以及该模型在一致算子拓扑意义下解的渐近行为,从而给出了该细菌种群的异步生长特性等结果.

In this paper,we study a class of structured bacterial population models under the boundary condition of total transition rule in L1 space.The spectral analysis of the transport operators in this model is discussed,and the weak compactness of the positive irreducible C0 semigroup generated by the transport operators is proved.It is concluded that the spectrum of the transport operator consists of only by at most countable isolate eigenvalues with finite algebraic multiplicities,and-∞is the only possible accumulation point,and the asymptotic behavior of the solution of the model in the topological sense of the uniform operator,so the asynchronous growth characteristics of the bacterial population are given.