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

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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 analysis of the model we designed with the experimental observations on which several branches of medicine are currently attempting to trade on their research activity.

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Acknowledgments

The authors would like to thank Prof. Nicola Guglielmi (Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila) for his support and helpful suggestions and discussions in setting up the numerical simulations in this paper.

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Authors and Affiliations

  1. DISIM, Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, 67100, L’Aquila, AQ, Italy

    Laura Di Bernardo & Donatella Donatelli

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  1. Laura Di Bernardo
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  2. Donatella Donatelli
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Correspondence to Donatella Donatelli.

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Communicated by Pierangelo Marcati.

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Di Bernardo, L., Donatelli, D. Global and local stability for a non-linear hyperbolic system model for the role of stem cells in physiological homeostasis. Comp. Appl. Math. 36, 1–22 (2017). https://doi.org/10.1007/s40314-014-0213-0

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  • DOI: https://doi.org/10.1007/s40314-014-0213-0

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