Spectral Distribution of Transport Operator Arising in Growing Cell Populations. (25th August 2014) - Wu, Hongxing; Wang, Shenghua; Yuan, Dengbin
Abstract : Transport equation with partly smooth boundary conditions arising in growing cell populations is studied inL p ( 1 < p < + ∞ ) space. It is to prove that the transport operatorA H generates aC 0 semigroup and the ninth-order remainder termR 9 ( t ) of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operatorA H consists of only finite isolated eigenvalues with finite algebraic multiplicities in a tripΓ ω . The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.