Research Of A Rotenberg Model In Cell Population

In this paper, we study a class of integral-differential transport equation in cell population in LP(1≤P<∞) space.We disscus that the constructive theory of the transport equation's solution,the properties of C0-semigroup which is governed by the Streaming operator and the asymptotic stability with different boundary conditions and so on.The main results are shown as follows:1.We study a Rotenberg model with smooth boundary condition inLP(1≤P<∞) space.Under the boundary condition is given by (1.2),we disscus that C0-semigroup which is governed by Streaming operator T,and give its explicit expression. We have proved that if the boundary operator is positive,strictly positive, the C0-semigroup which is generated by the Streaming operator T is positive, irreducible.And we obtain the existence of the eigenvalue of the transport operators A and the spectrum of the transport operators A only consist of finitely isolate eigenvalues with finite algebraic multiplicities in the trip Γs and other rusults.2.We study the Rotenberg model with unsmooth boundary condition in LP(1≤P<∞)space.Under the boundary condition is given by (1.4),we disscus that C0-semigroup which is governed by Streaming operator T,and give its explicit expression. We also discuss the positive, irreducible of the C0-semigroup which is generated by the streaming operator T.And if the boundary condition is some compact,we obtain that the eigenvalue of transpor operator A is not empty,the spectrum of the transport operator A only consist of finitely isolate eigenvalues with finite algebraic multiplicities in the trip Γs and other rusults.3. We study the model with general boundary condition in Lp(1≤P<∞). Under assume that the boundary condition is some compact, we obtain some results about the asymptotic stability and the asymptotic estimation of the Rotenberg model's solution about time t.