Spectral Analysis Research Of Rotenberg’s Transport Operators In Cell Population

The paper is studied a Rotenberg’s transport equation of cell population. It is to discuss that the spectral analysis, the properties of Co-semigroup which is governed by the transport operators and the asymptotic stability about time in different boundary conditions and so on. The main results are shown as follows:1. It is to discuss Rotenberg model of cell population in integral boundary condition, It is to prove that explicit expression of Co-semigroup TH(t) which is governed by operator T, It has proved that Co-semigroup TH (t) is positive irreducible and the existence of the eigenvalue of the transport operators A, and It is to obtain that the spectrum of the transport operators A only consist of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane and other results.2. It is to disscus Rotenberg model of cell population in general boundary condition, It is to prove that explicit expression of Co-semigroup TH(t)which is governed by Streaming operator T, It has proved that Co-semigroup TH(t) is positive irreducible and the existence of the eigenvalue of the transport operators A, and It is to obtain that the spectrum of the transport operators A only consist of finitely isolate eigenvalues with finite algebraic multiplicities in the right half plane and other results.3. It is to discuss Rotenberg model of cell population in general boundary condition, If the boundary operators is compact, It is proved that the asymptotic stability and the asymptotic estimation of the transport equation’s solution with Rotenberg model in cell population about time and other results.