Compactness for semigroups and application in growing cell populations
Renjie Hu · Journal of Liaoning Technical University · 2013
In order to obtain the spectral analysis of transport operator AK,this paper studied the equation of a certain kind of proliferating cell populations with an age structure in the L-R model.It is to prove that the corresponding transport operator AK could generate the C0 semigroup (VK(t))t≥0 in the condition of bounded boundary operator K;it is to prove that the C0 semigroup (VK(t))t≥0 is compact in the condition of boundary operator K being compact and positive;at last,it to obtain that the(K) A only consists of finite isolated eigenvalues which have a finite algebraic multiplicity.The main methods rely on the theory of semigroups of linear operators and solution method.