Well-posedness and asynchronous exponential growth of solutions of a two-phase cell division model

In this article we study a two-phase cell division model. The cells of the two different phases have different growth rates. We mainly consider the model of equal mitosis. By using the semigroup theory, we prove that this model is well-posed in suitable function spaces and its solutions have the property of asynchronous exponential growth as time approaches infinity. The corresponding model of asymmetric mitosis is also studied and similar results are obtained.