Here we consider the dynamics of a population of cells that are capable of simultaneous proliferation and maturation. The equations describing the cellular population numbers are first order partial differential equations (transport equations) in which there is an explicit temporal retardation as well as a nonlocal dependence in the maturation variable due to cell replication. The behavior of this system may be considered along the characteristics, and a global stability condition is proved.
A new theorem for asymptotic stability of Markov semigroups is proved. This result is applied to transport equations connected with diffusion and jumping processes and randomly perturbed dynamical systems. ᮊ
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