Abstract
This chapter discusses the growth of cell populations via one-parameter semigroups of positive operators. The description of the growth of a population by a mathematical equation marked the very beginning of mathematical biology. In the meantime, many more and highly sophisticated equations describing the growth of populations structured by age, size, or location have been proposed and analyzed. The chapter focuses on the mathematical theory behind many of these models. It presents the theory of one-parameter semigroups of positive operators that be applied to describe the asymptotic behavior of such cell populations. The spectral bound had to be less than or equal to zero to obtain convergence of the semigroup. For many models, only positive states allow a reasonable interpretation, and the time evolution is such that it yields only positive states once the initial state is positive.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
