Abstract:

With the help of linear operator theory, the transport equation with more general boundary condition for the structured equation with bacterial population as background is discussed. By means of resolving operator and comparison operator, it is proved that the corresponding transfer operator spectrum of the transfer equation consists of only a finite number of discrete eigenvalues with finite algebraic multiplicity in band domain $\Gamma_{\alpha, \beta}$. It is proved that the solution of the transfer equation is asymptotically stable when $\psi_0 \in D (A_{H_{\alpha, \beta}})$.

Key words: Bacterial population, Transport equation, Discrete eigenvalues, Asymptotic stability