Transport Equations With A Class Of Proliferating Cell Population

The objective of this paper is to research the transport equations of an age structured proliferating cell population with infinite cycle in Lp(1≤p<+00) space, It is discussed the spectral analysis of corresponding transport operators for this equation and the properties of the generated Co semigroup; and it is to obtain that the spectrum of the transport operators consists of countable isolate eigenvalues with finite algebraic multiplicities.The main results are showed below:1.It is discussed a mathematical model of L-R in Lp (1≤p<+∞) space. obtaining the positivity of the generated Co semigroup(VK(t))t≥0, and it is to obtain irreducibility of the generated Co semigroup (VK(t))t≥0.2. It is discussed the spectral analysis of corresponding transport operator AK for smooth transition operators with infinite cycle in Lp (1≤p<+∞) space, and it is to obtain that the spectrum of the transport operators consists of countable isolate eigenvalues with finite algebraic multiplicities.3. It is discussed the spectral analysis of corresponding transport operator AK for partly smooth transition operators with infinite cycle in Lp (1≤p<+∞) space, and it is to obtain that the spectrum of the transport operators consists of countable isolate eigenvalues with finite algebraic multiplicities.4. It is discussed a spectral decomposition of solutions of the Cauchy problem. And researched the asymptotically stable and asymptotically estimate about time t.