细菌种群增生中迁移算子占优本征值的存在性

The Existence of Dominant Eigenvalue of Transport Operators in Bacterial Population Proliferation

迁移算子的占优本征值的存在性是迁移理论中的一个重要的理论问题.这个问题与迁移方程解的大时间渐近行为密切相关.在L2空间中,运用线性算子理论,讨论了带一般边界条件下细菌种群增生的Rotenberg模型,采用构造算子、豫解算子等方法研究了相应迁移算子的谱分布情况,证明该迁移算子AH占优本征值的存在性.

The existence of dominant eigenvalues of transport operators is an important theoretical problem in transport theory.This problem is closely related to the large time asymptotic behavior of the solution of the transport equation.This article is in L2space,the Rotenberg model of bacterial population proliferation with general boundary conditions is discussed by using the linear operator theory.The spectral distribution of the corresponding transport operator is studied by using the methods of construction operator and resolvent operator,and it is to prove that the transport operator AHExistence of dominated eigenvalues.