Nonlinear semigroup approach to age structured proliferating cell population with inherited cycle length

This paper deals with a nonlinear semigroup approach to semilinear initial-boundary value problems which model nonlinear age structured proliferating cell population dynamics. The model involves age-dependence and cell cycle length, and boundary conditions may contain compositions of nonlinear functions and trace of solutions. Hence the associated operators are not necessarily formulated in the form of continuous perturbations of linear operators. A family of equivalent norms is introduced to discuss local quasidissipativity of the operators and a generation theory for nonlinear semigroups is employed to construct solution operators. The resultant solution operators are obtained as nonlinear semigroups which are not quasicontractive but locally equi-Lipschitz continuous.