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

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