在$L_p(1<p<\mathrm{\infty })$空间中, 用线性算子理论研究了细菌种群增生中具一般边界条件的Rotenberg模型, 采用比较算子和豫解算子等方法证明了算子$(\lambda I-B_H{)}^{-1}K$的紧性以及算子 $\mid Im\lambda \mid \parallel (\lambda I-B_H{)}^{-1}[K(\lambda I-B_H{)}^{-1}{]}^{m}K(\lambda I-A_H{)}^{-1}\parallel (|\mathrm{I}\mathrm{m}\lambda |\to +\mathrm{\infty })$在某带域中 的有界性, 得到了该相应迁移算子谱存在性和相应迁移方程解的渐近稳定性等结果.

In this paper, the Rotenberg model with general boundary conditions in bacterial population growth is discussed by using linear operator theory in $L_p(1<p<\mathrm{\infty })$ space. Compact operator $(\lambda I-B_H{)}^{-1}K$ and boundedness of operator $|\mathrm{I}\mathrm{m}\lambda \mid \parallel [(\lambda I-B_H{)}^{-1}K(\lambda I-B_H{)}^{-1}{]}^{m}K(\lambda I-A_H{)}^{-1}\parallel (|\mathrm{I}\mathrm{m}\lambda |\to +\mathrm{\infty })$ in a certain band domain are proved by using comparison operator and resolving operator. The results of spectral existence of the corresponding migration operator and asymptotic stability of the solution of the corresponding transport equation are obtained.