Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation

We present existence and uniqueness results for a proposed coupled nonlinear PDE–ODE model representing cancer population dynamics. We establish this global result using Banach fixed point theory. The model describes the evolution of two progenies of stem cell lineage consisting of healthy and mutat...

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Main Authors:	Iqra Batool, Naim Bajcinca
Format:	Article
Language:	English
Published:	Elsevier 2021-02-01
Series:	Results in Applied Mathematics
Subjects:	Well-posedness Fixed point Banach fixed point theorem Contraction mapping
Online Access:	http://www.sciencedirect.com/science/article/pii/S2590037420300455

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spelling	doaj-7921be38cd6d48ee8f738c9ab08afd732021-02-25T04:20:14ZengElsevierResults in Applied Mathematics2590-03742021-02-019100135Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulationIqra Batool0Naim Bajcinca1Corresponding author.; Mechanical and Process Engineering, University of Kaiserslautern, 67663 Kaiserslautern, GermanyMechanical and Process Engineering, University of Kaiserslautern, 67663 Kaiserslautern, GermanyWe present existence and uniqueness results for a proposed coupled nonlinear PDE–ODE model representing cancer population dynamics. We establish this global result using Banach fixed point theory. The model describes the evolution of two progenies of stem cell lineage consisting of healthy and mutated cells kept in homeostasis via feedback regulation. We also show continuous dependence of the solution on the initial data, concluding the original model’s well-posedness. Finally, we present numerical simulations of the model for illustration.http://www.sciencedirect.com/science/article/pii/S2590037420300455Well-posednessFixed pointBanach fixed point theoremContraction mapping
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Iqra Batool Naim Bajcinca
spellingShingle	Iqra Batool Naim Bajcinca Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation Results in Applied Mathematics Well-posedness Fixed point Banach fixed point theorem Contraction mapping
author_facet	Iqra Batool Naim Bajcinca
author_sort	Iqra Batool
title	Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation
title_short	Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation
title_full	Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation
title_fullStr	Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation
title_full_unstemmed	Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation
title_sort	well-posedness of a coupled pde–ode model of stem cell lineage involving homeostatic regulation
publisher	Elsevier
series	Results in Applied Mathematics
issn	2590-0374
publishDate	2021-02-01
description	We present existence and uniqueness results for a proposed coupled nonlinear PDE–ODE model representing cancer population dynamics. We establish this global result using Banach fixed point theory. The model describes the evolution of two progenies of stem cell lineage consisting of healthy and mutated cells kept in homeostasis via feedback regulation. We also show continuous dependence of the solution on the initial data, concluding the original model’s well-posedness. Finally, we present numerical simulations of the model for illustration.
topic	Well-posedness Fixed point Banach fixed point theorem Contraction mapping
url	http://www.sciencedirect.com/science/article/pii/S2590037420300455
work_keys_str_mv	AT iqrabatool wellposednessofacoupledpdeodemodelofstemcelllineageinvolvinghomeostaticregulation AT naimbajcinca wellposednessofacoupledpdeodemodelofstemcelllineageinvolvinghomeostaticregulation
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Well-posedness of a coupled PDE–ODE model of stem cell lineage involving homeostatic regulation

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