82 research outputs found
Global solutions for the one-dimensional Boussinesq-Peregrine system under small bottom variation
No full textThe Boussinesq-Peregrine system is derived from the water waves system in
presence of topographic variation under the hypothesis of shallowness and small
amplitude regime. The system becomes significantly simpler (at least in the
mathematical sens) under the hypothesis of small topographic variation. In this
work we study the long time and global well-posedness of the
Boussinesq-Peregrine system. We start by showing the intermediate time
well-posedness in the case of general topography (i.e. the amplitude of the
bottom graph ). The novelty resides in the functional setting,
. Then we show our main result
establishing that the global existence result obtained in
Molinet-Talhouk-Zaiter in the flat bottom case is still valid for the
Boussinesq-Peregrine system under the hypothesis of small amplitude bottom
variation (i.e. ). More precisely we prove that this system is
unconditionally globally well-posed in the Sobolev spaces of type . Finally, we show the existence of a weak
global solution in the Schonbek sense, i.e. existence of low regularity
entropic solutions of the small bottom amplitude Boussinesq-Pelegrine equations
emanating from and in an Orlicz class as weak
limits of regular solutions
An improved result for the full justification of asymptotic models for the propagation of internal waves
No full textWe consider here asymptotic models that describe the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with uneven bottoms. The aim of this paper is to show that the full justification result of the model obtained by Duchêne, Israwi and Talhouk [to appear in SIAM J. Math. Anal, (arXiv:1304.4554v2)], in the sense that it is consistent, well-posed, and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data, can be improved in two directions. The first direction is taking into account medium amplitude topography variations and the second direction is allowing strong nonlinearity using a new pseudo-symmetrizer, thus canceling out the smallness assumption of the Camassa-Holm regime for the existence and uniqueness results
Study of a coupled Cahn-Hilliard/Allen-Cahn system in phase separation
No full textCette thèse est une étude théorique d’un système d’équations de Cahn-Hilliard/Allen-Cahn couplées qui représente un mélange binaire en séparation de phase. Le but principal de l’étude est le comportement asymptotique des solutions en termes d’attracteurs exponentiels/globaux. Pour cette raison, l’existence et l’unicité de la solution sont étudiées tout d’abord. Une des principales applications de ce modèle d’équations est la cristallographie.Dans la première partie de la thèse, on examine le modèle proposé avec des conditions de type Dirichlet sur le bord et une non linéarité régulière de type polynomial : on réussit à trouver un attracteur exponentiel et par conséquence un attracteur global de dimension finie. Une non linéarité singulière de type logarithmique est ensuite prise dans la deuxième partie, cette fonction étant approchée par une suite de fonctions régulières et l’existence d’un attracteur global est démontrée sous des conditions au bord de type Dirichlet.Enfin, dans la dernière partie, le système est couplé avec une équation pour la température: suivant la loi de Fourrier premièrement, puis la loi de type III de la thermo-élasticité. Dans les deux cas, la dynamique de l’équation est étudiée et un attracteur exponentiel est trouvé malgré la difficulté créée par l’équation hyperbolique dans le deuxième cas.This thesis is a theoretical study of a coupled system of equations of Cahn-Hilliard and Allen-Cahn that represents phase separation of binary alloys. The main goal of this study is to investigate the asymptotic behavior of the solution in terms of exponential/global attractors. For this reason, the existence and unicity of the solution are first studied. One of the most important applications of this proposed model of equations is crystallography. In the first part of the thesis, the system is studied with boundary conditions of Dirichlet type and a regular nonlinearity (a polynomial). There, we prove the existence of an exponential attractor that leads to the existence of a global attractor of finite dimension. Then, a singular nonlinearity (a logarithmic potential) is considered in the second part. This function is approximated by a sequence of regular ones and a global attractor is found.At the end, the system of equations is coupled with temperature: with the Fourrier law in the first case, then with the type III law (in the context of thermoelasticity) in the second case. The dynamics of the equations are studied and the existence of an exponential attractor is obtained
Mathematical study of viscoelastic fluid flows in singular domains
No full textCette thèse est consacrée à l’analyse mathématique de trois problèmes d’écoulements de fluides viscoélastiques de type Oldroyd. Tout d’abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d’écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d’existence et d’unicité des solutions. Nous étudions également le cas d’un écoulement non stationnaire. Nous montrons un résultat d’existence locale et un résultat d’existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d’écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées"In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also establishe
Existence locale et unicité d'écoulements de fluides viscoélastiques dans des domaines non bornés
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Résultats d'existence pour les écoulements réguliers de fluides viscoélastiques incompressibles à loi différentielle de type White–Metzner en dimension 3
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Esercizio di sparizione. Liveness e performance mediata in The Perfumed Garden di Raafat Majzoub
No full textAt the Drodesera Festival / Supercontinent 2017 was presented Lebanese artist Raafat Majzoub’s installation The Perfumed Garden / Hekmat, xx. Part of a larger project to write a serial novel that originated in 2012 and has not yet been completed, in this stage Majzoub participates in the installation by writing a new chapter of the novel from his residence in Beirut. Unlike other performances that saw the author present, Hekmat, xx / Dro is confronted with a particular performative strategy that discusses the degree of presence/ absence of the artist, reconfigured through the mimetic passage in the narrative form and distant intervention. By updating a document shared on the GDrive platform and displayed on the screen of a laptop open on a desk, the artist makes visible to the user the act of creating a piece of text while not being physically present. The group of users visits and interacts (listening, watching, acting) in a physical space and enters into a specific and complex relationship with the author. Examining the artist’s critical writings and comparing them with theoretical sources, the essay investigates Majzoub’s project by analyzing an experiment that employs different degrees of mediated performance to express a series of artistic, philosophical and political instances.Al festival Drodesera / Supercontinent 2017 è stata presentata l’opera The Perfumed Garden / Hekmat, xx dell’artista libanese Raafat Majzoub. Parte di un più ampio progetto di scrittura di un romanzo seriale che ha avuto origine nel 2012 e che tuttora non è stato completato, in questa tappa Majzoub partecipa all’installazione scrivendo un nuovo capitolo del romanzo mentre si trova nella propria residenza a Beirut. A differenza di altre tappe che vedevano presente l’autore, Hekmat, xx / Dro si confronta con una particolare modalità di fruizione che discute il grado di presenza/assenza dell’artista, riconfigurato attraverso il passaggio mimetico nella forma narrativa e l’intervento a distanza. Aggiornando in tempo reale un documento condiviso sulla piattaforma Google Drive che viene visualizzato sullo schermo di un laptop, l’artista rende visibile al fruitore l’atto di creazione di un brano di testo pur non essendo fisicamente presente. Il gruppo dei fruitori abita e interagisce (ascoltando, guardando, agendo) in uno spazio fisico ed entra in una specifica e complessa relazione con l’autore. Esaminando gli scritti critici dell’artista e confrontandoli con formulazioni teoriche, il saggio analizza il progetto di Majzoub approfondendo un esperimento che impiega diversi gradi della performance mediata per esprimere una serie di istanze artistiche, filosofiche e politiche
A lover's discourse : fictions
No full textThesis: S.M. in Art, Culture and Technology, Massachusetts Institute of Technology, Department of Architecture, 2017.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis. "June 2017."Includes bibliographical references (pages 130-131).This thesis sets a landscape to discuss intimacy as a political tool, using fiction as a methodology to create potency in the Arab world. Its concern with critique is on the actionable level. This document discusses projects that critique realities in Lebanon and the Arab World by proposing (1) that these realities are in fact fictions (2) that can be contested by creating new fictions through cultural practice. The arguments, challenges and defenses happen in public through observations and readings. The corpus of this thesis is the manuscript of a novel written between 2012 and 2015, "The Perfumed Garden: An Autobiography of Another Arab World," and the methodology of writing it.by Raafat Majzoub.S.M. in Art, Culture and Technolog
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