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

TL;DR

This paper develops a mathematical model using non-linear hyperbolic conservation laws to analyze stem cell dynamics in tissue homeostasis, providing theoretical stability results aligned with experimental observations.

Contribution

It introduces a new existence and uniqueness theory for a complex hyperbolic system modeling stem cell behavior in tissue homeostasis.

Findings

Stability results are consistent with experimental data.

The model offers a rigorous mathematical framework for stem cell research.

The approach bridges theoretical analysis with practical biological observations.

Abstract

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.