Spectral Distribution of Transport Operator Arising in Growing Cell Populations

Transport equation with partly smooth boundary conditions arising in growing cell populations is studied inLp (1<p<+∞)space. It is to prove that the transport operatorAHgenerates aC0semigroup and the ninth-order remainder termR9(t)of the Dyson-Phillips expansion of the semigroup is compact, and the spectrum of transport operatorAHconsists of only finite isolated eigenvalues with finite algebraic multiplicities in a tripΓω. The main methods rely on theory of linear operators, comparison operators, and resolvent operators approach.