A Viscoelastic Model with  Non-local Damping: Application to the Human Lungs

Grandmont, Céline; Maury, Bertrand; Meunier, Nicolas

dc.contributor.author	Grandmont, Céline
dc.contributor.author	Maury, Bertrand
dc.contributor.author	Meunier, Nicolas
dc.date.accessioned	2011-05-09T08:40:46Z
dc.date.available	2011-05-09T08:40:46Z
dc.date.issued	2006
dc.identifier.uri	https://basepub.dauphine.fr/handle/123456789/6210
dc.language.iso	en	en
dc.subject	Poiseuille flow	en
dc.subject	dyadic tree	en
dc.subject	kernel operator	en
dc.subject	damped wave equation	en
dc.subject	human lungs	en
dc.subject.ddc	515	en
dc.title	A Viscoelastic Model with Non-local Damping: Application to the Human Lungs	en
dc.type	Article accepté pour publication ou publié
dc.description.abstracten	In this paper we elaborate a model to describe some aspects of the human lung considered as a continuous, deformable, medium. To that purpose, we study the asymptotic behavior of a spring-mass system with dissipation. The key feature of our approach is the nature of this dissipation phenomena, which is related here to the flow of a viscous fluid through a dyadic tree of pipes (the branches), each exit of which being connected to an air pocket (alvelola) delimited by two successive masses. The first part focuses on the relation between fluxes and pressures at the outlets of a dyadic tree, assuming the flow within the tree obeys Poiseuille-like laws. In a second part, which contains the main convergence result, we intertwine the outlets of the tree with a spring-mass array. Letting again the number of generations (and therefore the number of masses) go to infinity, we show that the solutions to the finite dimensional problems converge in a weak sense to the solution of a wave-like partial differential equation with a non-local dissipative term.	en
dc.relation.isversionofjnlname	Modélisation mathématique et analyse numérique
dc.relation.isversionofjnlissue	40	en
dc.relation.isversionofjnldate	2006
dc.relation.isversionofjnlpages	201-224	en
dc.relation.isversionofdoi	http://dx.doi.org/10.1051/m2an:2006009	en
dc.description.sponsorshipprivate	oui	en
dc.relation.isversionofjnlpublisher	EDP Sciences	en
dc.subject.ddclabel	Analyse	en

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