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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Integrability of Second-Order Partial Differential Equations and the Geometry of GL(2)-Structures

Smith, Abraham David January 2009 (has links)
<p>A GL(2,R)-structure on a smooth manifold of dimension n+1 corresponds to a distribution of non-degenerate rational normal cones over the manifold. Such a structure is called k-integrable if there exist many foliations by submanifolds of dimension k whose tangent spaces are spanned by vectors in the cones.</p><p>This structure was first studied by Bryant for n=3 and k=2. The work included here (n=4 and k=2,3) was suggested by Ferapontov, et al., who showed that the cases (n=4,k=2) and (n=4, k=3) can arise from integrability of second-order PDEs via hydrodynamic reductions.</p><p>Cartan--Kahler analysis for n=4 and k=3 leads to a complete classification of local structures into 54 equivalence classes determined by the value of an essential 9-dimensional representation of torsion for the GL(2,R)-structure. These classes are described by the factorization root-types of real binary octic polynomials. Each of these classes must arise from a PDE, but the PDEs remain to be identified. </p><p>Also, we study the local problem for n >= 5 and k=2,3 and conjecture that similar classifications exist for these cases; however, the interesting integrability results are essentially unique to degree 4. The approach is that of moving frames, using Cartan's method of equivalence, the Cartan--Kahler theorem, and Cartan's structure theorem.</p> / Dissertation
2

Sufficient conditions for local exactness of the exact penalty function method in nonsmooth optimization

Al hashimi, Farah 01 May 2019 (has links)
No description available.
3

Inclusions différentielles d'évolution associées à des ensembles sous-lisses / Evolution differential inclusions associated with subsmooth sets

Noel, Jimmy 23 May 2013 (has links)
Cette thèse est consacrée à l'étude d'existence de solutions pour certains problèmes d'évolution. Il s'agit de processus de rafle perturbés associés d'une part à des ensembles prox-réguliers et d'autre part à des ensembles sous-lisses. Les ensembles sont supposés évoluer de façon lipschitzienne ou absolument continue. / This dissertation is devoted to the study of the existence of solutions for some evolution problems. The study is concerned with perturbed sweeping processes associated on the one hand with prox-regular sets and the other hand with subsmooth sets. It is assumed that the sets move either in a Lipschitz way or in an absolutely continuous way.
4

Ensembles localement prox-réguliers et inéquations variationnelles / Locally prox-regular sets and variational inequalities

Mazade, Marc 30 November 2011 (has links)
Les propriétés des ensembles localement prox-réguliers ont été étudiées par R.A. Poliquin, R.T. Rockafellar et L. Thibault. Le concept de fonction ''primal lower nice'' a été introduit en dimension finie par R.A. Poliquin et étendu au cadre Hilbertien par A.B. Levy, R.A. Poliquin et L. Thibault. Dans cette thèse, la première partie est consacrée à une étude des outils et des objets géométriques de l'Analyse non lisse tels que les fonctions primal lower nice et les ensembles localement prox-réguliers. On donnera une définition quantifiée de la prox-régularité locale. La deuxième partie établit des résultats d'existence et d'unicité de solutions d'inéquations variationnelles se présentant sous forme d'inclusions différentielles associées au cône normal d'un ensemble localement prox-régulier. / The properties of locally prox-regular sets have been studied by R.A. Poliquin, R.T. Rockafellar and L. Thibault. R.A. Poliquin also introduced the concept of ``primal lower nice function. This dissertation is devoted, on one hand to the study of primal lower nice functions and locally prox-regular sets and, on the other hand, to show existence and uniqueness of solutions of differential variational inequalities involwing such sets. Concerning the first part, we introduce a quantified viewpoint of local-prox-regularity and establish a series of characterizations for set satisfying this property. In the second part, we study differential variational inequalities with locally prox-regular sets and we show the relevance of our quantified viewpoint to prove existence results of solutions.
5

Hierarchické úlohy s evolučními ekvilibriálními omezeními / Hierarchical Problems with Evolutionary Equilibrium Constraints

Adam, Lukáš January 2015 (has links)
Title: Hierarchical Problems with Evolutionary Equilibrium Constraints Author: Lukáš Adam Supervisor: Prof. Jiří Outrata Abstract: In the presented thesis, we are interested in hierarchical models with evolutionary equilibrium constraints. Such models arise naturally when a time-dependent problem is to be controlled or if parameters in such a model are to be identified. We intend to discretize the problem and solve it on the basis of the so-called implicit programming approach. This technique requires knowledge of a generalized derivative of the solution mapping which assigns the state variable to the control variable/parameter. The computation of this generalized derivative amounts equivalently to the computation of (limiting) normal cone to the graph of the solution mapping. In the first part we summarize known techniques for computation of the normal cone to the set which can be represented as a finite union of convex polyhedra. Then we propose a new approach based on the so-called normally admissible stratification and simplify the obtained formulas for the case of time-dependent problems. The theoretical results are then applied first to deriving a criterion for the sensitivity analysis of the solution mapping and then to the solution of two practically motivated problems. The first one concerns optimal...
6

Deformation groupoids and applications / Groupoïdes de déformations et applications

Mohsen, Omar 04 October 2018 (has links)
Cette thèse est consacrée à l’étude de trois questions différentes concernant les groupoïdes de Lie et leurs applications. Le premier chapitre présente quelques préliminaires sur les groupoïdes de Lie. Dans le chapitre 2, on exprime la déformation de Witten à l’aide d’une déformation au cone normal et la théorie de C∗-modules ce qui nous permet de retrouver les inégalités de Morse. Notre méthode se généralise au cas des feuilletages. Dans le chapitre 3, on donne une construction simple du groupoïde de déformation construit par Choi-Pönge et Van Erp-Yuncken. Rappelons que celui-ci décrit le calcule pseudo-différentiel inhomogène grâce au travail de Debord-Skandalis et Van Erp- Yuncken. Notre construction montre que le groupoïde de déformation est en fait une déformation au cone normal classique itérée. Dans le chapitre 4, suivant le travail de Antonini, Azzali et Skandalis, on construit un élément en KK-théorie équivariante qui permet d’exprimer directement les invariants de Chern-Simons en K-théorie. Dans l’appendice on donne quelques rappels sur la KK-théorie équivariante et la KK-théorie réelle introduite par Antonini, Azzali et Skandalis. / This thesis is devoted to the study of three different questions concerning Lie groupoids and their applications. The first chapter presents some preliminaries on Lie groupoids. In Chapter 2, Witten’s deformation is expressed using deformation to the normal cone construction and the theory of C∗-modules, which allows us to reprove the Morse inequalities. Our method is generalised to the case of foliations. In Chapter 3, we give a simple construction of the deformation groupoid built by Choi-Pönge and Van Erp-Yuncken. Recall that this groupoid describes the inhomogeneous pseudo-differential calculus thanks to the work of Debord-Skandalis and Van Erp-Yuncken. Our construction shows that the deformation groupoid is actually an iterated classical deformation to the normal cone. In Chapter 4, following the work of Antonini, Azzali and Skandalis, we construct an element in equivariant KK-theory that allows us to express the Chern-Simons invariants directly in K-theory. In the appendix we give some reminders about the equivariant KK-theory and the real KK-theory introduced by Antonini, Azzali and Skandalis.
7

Contribution à l'analyse variationnelle : stabilité des cônes tangents et normaux et convexité des ensembles de Chebyshev / Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

Zakaryan, Taron 19 December 2014 (has links)
Le but de cette thèse est d'étudier les trois problèmes suivantes : 1) On s'intéresse à la stabilité des cônes normaux et des sous-différentiels via deux types de convergence d'ensembles et de fonctions : La convergence au sens de Mosco et celle d'Attouch-Wets. Les résultats obtenus peuvent être vus comme une extension du théorème d'Attouch aux fonctions non nécessairement convexes sur des espaces de Banach localement uniformément convexes. 2) Pour une bornologie β donnée sur un espace de Banach X, on étudie la validité de la formule suivante (…). Ici Tβ(C; x) et Tc(C; x) désignent le β -cône tangent et le cône tangent de Clarke à C en x. On montre que si, X x X est ∂β-« trusted » alors cette formule est valable pour tout ensemble fermé non vide C ⊂ X et x ∈ C. Cette classe d'espaces contient les espaces ayant une norme équivalent β-différentiable, etplus généralement les espaces possédant une fonction "bosse" lipschitzienne et β-différentiable). Comme conséquence, on obtient que pour la bornologie de Fréchet, cette formule caractérise les espaces d'Asplund. 3) On examine la convexité des ensembles de Chebyshev. Il est bien connu que, dans un espace normé réflexif ayant la propriété Kadec-Klee, tout ensemble de Chebyshev faiblement fermé est convexe. On démontre que la condition de faible fermeture peut être remplacée par la fermeture faible locale, c'est-à-dire pour tout x ∈ C il existe ∈ > 0 tel que C ∩ B(x, ε) est faiblement fermé. On montre aussi que la propriété Kadec-Klee n'est plus exigée lorsque l'ensemble de Chebyshev est représenté comme une union d'ensembles convexes fermés. / The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to C at x. We proved that it holds true for every closed set C ⊂ X and any x ∈ C, provided that the space X x X is ∂β-trusted. The trustworthiness includes spaces with an equivalent β-differentiable norm or more generally with a Lipschitz β-differentiable bump function. As a consequence, we show that for the Fréchet bornology, this "lim inf" formula characterizes in fact the Asplund property of X. 3) We investigate the convexity of Chebyshev sets. It is well known that in a smooth reflexive Banach space with the Kadec-Klee property every weakly closed Chebyshev subset is convex. We prove that the condition of the weak closedness can be replaced by the local weak closedness, that is, for any x ∈ C there is ∈ > 0 such that C ∩ B(x, ε) is weakly closed. We also prove that the Kadec-Klee property is not required when the Chebyshev set is represented by a finite union of closed convex sets.

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