Global and Local stability for a non-linear hyperbolic system model for the role of stem cells in physiological homeostasis

In this paper we propose an existence and uniqueness theory for the solutions of a system of non-linear hyperbolic conservation laws, structured in age and maturity variables, representing a tissue environment. In particular we are interested in the investigation of the role of stem cells in its homeostasis. The main result presented in this paper is the consistence of the stability results arising from the analisys of the model we designed with the experimental observations on which several branches of medicine are currently attempting to trade on their research activity.