Skip to Main content Skip to Navigation
Theses

Contribution à l'étude d'une équation de transport à retards décrivant une dynamique de population cellulaire

Abstract : We present a model of blood cell division based on two biological hypotheses : the presence of a factor called maturation and the division of the cycle into a resting and a proliferating phase It is represented by a system S of two age-maturity structured semi linear transport equations. Integrating with respect to the age, S becomes a system of maturity structured partial differential equations with delays. In chapter 1, we introduce the biological background motivating our work, and we present our model. In chapter 2, we study the model where the proliferating phase is constant and the cell division is equal. We prove a result of existence and uniqueness, then we show a result linking the solutions to the stem cells. We prove invariance, and asymptotic behaviour results and instability. In chapter 3, the proliferating phase depends on the cell maturity. We prove similar results as in chapter 2. In chapter 4, the proliferating phase is fixed but cells do not divide in an equal way. Using the Markov operator theory, we prove a global stability result.
Document type :
Theses
Complete list of metadatas

Cited literature [128 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00001176
Contributor : Laurent Pujo-Menjouet <>
Submitted on : Thursday, February 28, 2002 - 5:28:58 PM
Last modification on : Tuesday, February 2, 2021 - 2:54:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 6:12:23 PM

Identifiers

  • HAL Id : tel-00001176, version 1

Collections

Citation

Laurent Pujo-Menjouet. Contribution à l'étude d'une équation de transport à retards décrivant une dynamique de population cellulaire. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2001. Français. ⟨tel-00001176⟩

Share

Metrics

Record views

319

Files downloads

670