dc.contributor.author Cid-Montiel, Lorena dc.date.accessioned 2017-01-23 17:29:40 (GMT) dc.date.available 2017-01-23 17:29:40 (GMT) dc.date.issued 2017-01-23 dc.date.submitted 2016-11-29 dc.identifier.uri http://hdl.handle.net/10012/11242 dc.description.abstract In this work we present some of the geometric constructs that aid the application of en the Ważewski Theorem. To illustrate the procedure the Michaelis-Menten mechanism will be considered. We show that M, a slow manifold, exists and is fully contained in a given set V . The set V must satisfy that its set of ingress points I with respect to de differential system of equations are strict. The Ważewski Theorem asserts that if the subset of strict ingress points of V is not a retract of the whole set then there exist a trajectory φ contained in V for all positive/negative values of time. More specifically, the theorem establishes that if we can find a set Z ⊂ V ∪ I such that Z ∩ I is a retract of I but not a retract of Z then φ exists. For the construction of the set V the existence of continuously differentiable functions which behave similarly to Liapunov functions on some parts of their zero-levels is required. The starting point to define such functions was to use the expressions obtained from the quasi steady state and rapid equilibrium assumptions (QSSA and REA). One surprising property of M is that it is the only trajectory that stays in the set V . To discuss uniqueness of the slow manifold we show the following two conditions are satisfied: • One of the coordinates, let us say xi is monotone and 0 < xi < ∞. The cross-section given by xi constant has either a non-decreasing or fixed diameter as xi increases. • The distance between two different solutions in V is non-decreasing as xi increases. with respect to a chosen variable, any two solutions in the polyfacial set V are always moving apart and the diameter of the cross sections of V is either decreasing or constant. dc.language.iso en en dc.publisher University of Waterloo en dc.subject Ważewski principle en dc.subject Retract method en dc.subject Slow invariant manifolds en dc.title Existence and uniqueness of attracting slow manifolds: An application of the Ważewski principle en dc.type Master Thesis en dc.pending false uws-etd.degree.department Applied Mathematics en uws-etd.degree.discipline Applied Mathematics en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Master of Mathematics en uws.contributor.advisor Siegel, David uws.contributor.affiliation1 Faculty of Mathematics en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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