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Raafat Khalil Talhouk

Full professor
Mathematics department - Section I - Hadath
Speciality: Mathematics
Specific Speciality: Analyse / EDP

Positions
2016 - present : Membre du comité éditorial du journal: "AIMS Mathematics" http://www.aimspress.com/journal/Math

2013 - present : Membre du comité central de direction de l'evaluation de la recherche et des thèses

Université Libanaise
Hadath

2012 - present : Membre du comite éditorial du journal :Discrete and continuous Dynamical Systems-Serie S(DCDS-S)\\ https://aimsciences.org/journals/home.jsp?journalID=15

2011 - present : Directeur du laboratoire de mathématiques-EDST

Université Libanaise-Ecole doctorale des sciences et de technologies
Hadath

2010 - present : Membre du conseil scientifique

Université Libanaise-Ecole doctorale des sciences et de technologies
Hadath

2007 - present : Responsable du Master 2-specialité EDP et Analyse numérique

Université Libanaise-Faculté des sciences
Hadath

2007 - present : Membre du comité de direction de la recherche de l'EDST

Université Libanaise-Ecole doctorale des sciences et de technologies
Hadath

2004 - present : Membre de la commission des spécialistes

Université Libanaise-Faculté des sciences
Hadath

2009 - 2011 : Membre élu au conseil de direction du département de mathématiques de la faculté des sciences

Université Libanaise-Faculté des sciences
Hadath

2004 - 2007 : Membre du comité central de direction de la recherche scientifique

Université Libanaise
Hadath

1999 - 2000 : Directeur du département de mathématiques de la faculté des sciences 1

Université Libanaise-Faculté des sciences
Hadath

1994 - 1996 : Attaché temporaire d'enseignement et de recherche

Université Paris 12 Créteil
Paris -France

1991 - 1994 : Allocateur de recherche et moniteur de l'enseignement supérieur

Université Paris-sud Orsay
Orsay-France

Teaching 5 Taught Courses
(2014-2015) Math 403 - Distribution theory

M1 Mathematics

(2014-2015) Math 403 - Distribution theory

M1 Mathematics

(2014-2015) MATH 502 - Analysis for PDE's

M2 Partial Differential Equations and Numerical Analysis

(2014-2015) MEDP 506 - Asymptotic models in oceanography

M2 Partial Differential Equations and Numerical Analysis

(2014-2015) Math 407 - Partial differential equations

M1 Mathematics

Education
1991 - 1994: Doctorat

Université Paris XI, Orsay (France)
PDE's and Nonlinear Analysis

1990 - 1991: DEA

Université Paris XI, Orsay (France)
Analyse numérique et applications

DEA

1989 - 1990: Maitrise

Université Paris XI, Orsay (France)
Mathématique

Maitrise

1988 - 1989: Licence

Université Paris XI, Orsay (France)
Mathématique

1986 - 1988: DEUG "A"

Université Paris XII, Créteil (France)
Sciences des structures et de la matière

1985 - 1986: Classe préparatoire

Lycée Eiffel, Cachan (France)
Maths Sup Technologique

1984 - 1985: Baccaleauréat

Lycée Romain Rolland, Ivry sur Seine (France)
Mathématique et Sciences générales

Conferences 19 participations
A coupled anisotropic chemotaxis fluid model: Mathematical and numerical analysis

Seminar
2014-12-17

" Fifth Annual Conference " of the Lebanese society for Mathematical Sciences

Plenary session
2014-06-06 to 2014-06-07

Mécaniques des fluides:aspect déterministes et stochastiques

Plenary session
2013-09-13

A new Green Naghdi model in the camassa-Holm regimeand full justification of internal waves models

Seminar
2013-09-12

Slightly compressible viscoelastic fluid flows and the incompressible limite

Seminar
2013-09-02

Etats de la recherche "Topics on Compressible fluids"

Conference
2012-05-21 to 2015-05-25

On the singularities problem in some linear PDE's in polygonal domains

Seminar
2010-10-16

Conference on Biomathematics:Newtonian limit for weakly viscoelastic fluids flows of Oldryd type

Conference
2007-06-26 to 2007-06-28

Sur les resultas recents en fluides non-newtonien et problemes ouverts

Seminar
2004-03-08

Généralisation de l'existence globale de solutions des ecoulements de fluides viscoelastiques de type Oldroyd

Summer School
2002-07-08 to 2002-07-11

Sur l'existence global des écoulements de fluides viscoélastiques de type Oldroyd

Seminar
2002-02-17

L'existence de solutions des ecoulements de fluides viscoelastiques de type Jeffreys autour d'un obstacle

Seminar
2001-09-04

Les problèmes d'exitence d'écoulements de fluides viscoélastiques autour d'un obstacle

Seminar
1999-06-02

Ecoulements stationnaires de fluides viscoléastiques faiblement compressibles

Congress
1994-04-16

Ecoulements non stationnaires de fluides viscoelastiques de type Jeffreys et hyperbolicité du modèle de Maxwell

Seminar
1994-03-16

Ecoulements faiblement compressibles de fluides viscoélastiques

Congress
1994-02-16

Les écoulements dans un canal borne aux conditions avec limites rentrantes sortantes

Seminar
1994-02-16

Third Winter School of Paseky-Tcheque republic

Congress
1993-05-16

Existence d;ecoulemens de fluides viscelastiques dans un domaine non borné

Congress
1993-04-12

Publications 23 publications
With V. Duchene and S. Israwi A new class of two-layer Green-Naghdi systems with improved frequency dispersion Studies in Applied Mathematics (SAPM) 2016

With H. Alrachid and T. Leli\`evre Local and global solutions for a nonlocal Fokker-Planck equation related to the adaptive biasing force process J. Differential Equations 2016

With S. Israwi and R. Lteif An improved Green-Naghdi model for the full justification of asymptotic models for the propagation of internal waves Comm. Pure and Appl. Anl. 2015

Vincent duchene, Samer Israwi A new fully justified asymptotic model for the propagation of internal waves in the Camassa-Holm regimes SIAM J.Math.Anal.47(2015),no.1,240-290 2015

This study deals with asymptotic models for 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 a flat bottom. We present a new Green--Naghdi type model in the Camassa--Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent and well-posed and that its solutions remain close to exact solutions of the full Euler system with corresponding initial data. Moreover, our system allows one to fully justify any well-posed and consistent lower order model, and, in particular, the so-called Constantin--Lannes approximation, which extends the classical Korteweg--de Vries model to the Camassa--Holm regime.

Georges Chamoun, Mazen Saad A coupled anisotropic chemotaxis-fluid model:the case of two-sidely degenerate diffusion Computers and mathematics with applications,Vol 68,No.9,pp. 2052-2070 2014

In this article, the mathematical analysis of a model arising from biology consisting of diffusion, chemotaxis with volume filling effect and transport through an incompressible fluid, is studied. Motivated by numerical and modeling issues, the global-in-time existence of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of two-sidedly nonlinear degenerate diffusion and of anisotropic and heterogeneous diffusion tensors where we prove the global existence for a Chemotaxis-Navier–Stokes system in space dimensions less than or equal to four and we show the uniqueness of weak solutions for the Chemotaxis-Stokes system in two or three space dimensions under further assumptions.

Georges Chamoun, Mazen Saad Monotone combined edge Finite element Scheme for anisotropic Keller-Segel Model Numerical Methods for Partial Differential Equations,30, No 3,1030-1065 2014

In this article, a new numerical scheme for a degenerate Keller–Segel model with heterogeneous anisotropic tensors is treated. It is well-known that standard finite volume scheme not permit to handle anisotropic diffusion without any restrictions on meshes. Therefore, a combined finite volume-nonconforming finite element scheme is introduced, developed, and studied. The unknowns of this scheme are the values at the center of cell edges. Convergence of the approximate solution to the continuous solution is proved only supposing the shape regularity condition for the primal mesh. This scheme ensures the validity of the discrete maximum principle under the classical condition that all transmissibilities coefficients are positive. Therefore, a nonlinear technique is presented, as a correction of the diffusive flux, to provide a monotone scheme for general tensors. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1030–1065, 2014

Vincent duchene, Samer Israwi Shallow water asymptotic models for the propagation of internal waves Discrete and continuous Dynamical Systems Series S,Vol 7, N0.2,pp.239-269 2014

We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order to offer a unified and comprehensive exposition. Anterior models such as the shallow water and Boussinesq systems, as well as unidirectional models of Camassa-Holm type, are shown to descend from a broad Green-Naghdi model, that we introduce and justify in the sense of consistency. Contrarily to earlier works, our Green-Naghdi model allows a non- at topography, and horizontal dimension d = 2. Its derivation follows directly from classical results concerning the one-layer case, and we believe such strategy may be used to construct interesting models in di erent regimes than the shallow- water/shallow-water studied in the present work.

Georges Chamoun, Mazen Saad finite volume scheme for isotropic Keller-Segel model with general sclar diffusive functions ESAIM:PROCEEDINGS, September 2014,Vol.45 p.128-137 2014

This paper is devoted to the numerical analysis of a modified Keller-Segel model consisting of diffusion and chemotaxis with volume filling effect. Firstly, a finite volume scheme is generalized to the case of a Keller-Segel model allowing heterogeneities and discontinuities in the diffusion coefficients. For that, we start with the derivation of the discrete problem and then we establish a convergence result of the discrete solution to a weak solution of the continuous model. Finally, numerical tests illustrate the behavior of the solutions of this generalized numerical scheme.

Samer Israwi Local well-posedness of a nonlinear KDV-type equation, C. R. Acad.Sci. Paris, Ser.A. 351.pp 895-899 2013

In this paper, a generalized nonlinear KdV equation with time- and space-dependent coefficients is considered. We show that the control of the dispersive and “diffusion” terms is possible if we use an adequate weight function determined with respect to the dispersive and “diffusion” coefficients to define the energy. We use the dispersive properties of the equation to prove the existence and uniqueness of solutions.

Georges Chamoun, Mazen Saad Mathematical analysis of a modified Keller-Segel model with general diffusive tensors Biomath 2 1312071,1-6 2013

This paper is devoted to the mathematical analysis of a model arising from biology, consisting of diffusion and chemotaxis with volume filling effect. Motivated by numerical and modeling issues, the global existence in time and the uniqueness of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of a two-sidedly nonlinear degenerate diffusion and anisotropic heterogeneous diffusion tensors, where we prove global existence and uniquenessunder further assumptions. Moreover, we introduce and we study the convergence analysis of the combined scheme applied to this anisotropic Keller-Segel model with general tensors. Finally, a numerical test is given to prove the effectiveness of the combined scheme.

Colette Guillopé, Zeinab Salloum Existence results for flows of slightly compressible viscoelastic fluid in a bounded domain with corners Anal.Appl.(Singap.)10,no. 4,381-411 2012

Steady flows of slightly compressible viscoelastic fluids of Oldroyd’s type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces V ξ k , where the index ξ characterizes the power growth of the solution near the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part ∇ φ

Colette Guillopé, Zeinab Salloum Regular flows of weakly compressible viscoelastic fluids and the incompressible limit Disc. Cont. Dyn. Syst.B (DCDS-B),Vol. 14,No.3,pp.1001-1028 2010

We consider compressible viscoelastic fluids satisfying the Oldroyd constitutive law. We prove the local existence (and uniqueness) of flows by a classical fixed point argument. We also prove some global properties of the solutions. In particular, we obtain some a priori estimates which are uniform in the Mach number and prove global existence of weakly compressible fluids flows. We show that weakly compressible flows with well-prepared initial data converge to incompressible ones when the Mach number converges to zero.

Luc Molinet Newtonian limit for weakly viscoelastic fluids flows of Oldroy's type SIAM Journal of Mathematical Analysis, Vol. 39,No. 5,pp.23-43 2008

This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in $\R^N$ or $\T^N$ for N=2,3, when the Weissenberg number (relaxation time measuring the elasticity effect in the fluid) tends to zero. More precisely, we prove that the velocity field and the extra-stress tensor converge in their existence spaces (we examine the Sobolev-Hs theory and the Besov-Bs,12 theory to reach the critical case s=N/2) to the corresponding newtonian quantities. These convergence results are established in the case of "ill-prepared"' data.We deduce, in the two-dimensional case, a new result concerning the global existence of weakly viscoelastic fluids flow. Our approach makes use of essentially two ingredients : the stability of the null solution of the viscoelastic fluids flow and the damping effect,on the difference between the extra-stress tensor and the tensor of rate of deformation, induced by the constitutive law of the fluid.

Colette Guillopé, Abdellilar Hakim Existence of steady flows of slightly compressible viscoelastic fluids of White-Metzner type around an obstacle Communication in Pure and Applied Analysis, Vol.4,Nu. 1,pp.23-43 2005

This work is concerned with the study of steady flows, around an obstacle, of slightly compressible viscoelastic fluids, for which the extra-stress tensor is given by a White-Metzner constitutive law. The existence and uniqueness of such flows are shown, when Newtonian viscosity is present (Jeffreys' model), and for small data.

Luc Molinet Existence and stability results for3-D regular flows of viscoelastic fluids of White-Metzner type Nonlinear Analysis,TMA, Vol.58, Nu. 7-8,pp.816-833 2004

This paper is concerned with regular flows of incompressible viscoelastic fluids which obey a differential constitutive law of White–Metzner type. We study the existence and uniqueness of local solutions in 3-D domain as well as the global existence for small data. By a classical stability argument, we deduce the existence and stability of small periodic and stationary solutions. We also generalize the 2-D results. More precisely, we prove that the results obtained by Hakim (J. Math. Anal. Appl. 185 (1994) 675) remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity (Navier–Stokes equation) and the transport equation verified by the extra-stress tensor. The hypothesis of boundedness on the relaxation function is also dropped.

Luc Molinet Resultas d'existence pour les ecoulements reguliers de fluides viscoelstiques incompressibles a loi diffrentielle de type Metzner en dimension 3 C. R. Acad.Sci. Paris, Ser.I 338.pp 171-176 2004

This paper is concerned with incompressible viscoelastic fluids which obey a differential constitutive law of White-Metzner type. We establish the existence and uniqueness of local solutions in 3-D as well as the global existence of small solutions. We then deduce the existence and asymptotic stability of small periodic and stationary solutions. Finally, we prove that the 2-D results obtained in Hakim (J. Math. Anal. Appl. 185 (1994) 675-705) remain true without any restriction on the smallness of the retardation parameter which is the linking coefficient between the equation of velocity (Navier-Stokes equation) and the transport equation verified by the extra-stress tensor. To cite this article: L. Molinet, R. Talhouk, C. R. Acad. Sci. Paris, Ser. I 338 (2004

Luc Molinet On the global and periodic regular flows of viscoelastic fluids with differential constitutive law Nonlinear differential equations&applications Vo 11, Nu.3,pp.349-359 2004

This paper is concerned with the existence and uniqueness of global, periodic and stationary solutions for flows of incompressible viscoelastic fluids for which the extra-stress tensor satisfies a differential constitutive law. More precisely, we prove that the results obtained by C Guillopé and J.C. Saut [5] remain true without any restriction on the smallness of the retardation parameter.

Colette guillopé Steady flows of slightly compressible viscoelastic fluid flows of Jeffreys type around an obstacle Differential &integral equations, vol 16,Ni.11,pp.1293-1320 2003

We consider steady flows of slightly compressible viscoelastic fluids for which the extra-stress tensor is given by a differential constitutive equation. We examine the effect, on the flows, of compressibility. In particular, we show the existence of a unique solution to the 3-D steady boundary value problem, in the case of a nonzero Newtonian viscosity (Jeffreys' type fluids).

Colette guillopé, Ali Mneimné Asymptotic behavior,with respect to the isothermal compressibilty coefficient, for steady flows of weakly compressible viscoelastic fluids Asymptotic analysis,vol.35,Nu.2,pp.127-150 2003

In this paper, we study the behaviour, in terms of compressibility, of steady flows of weakly compressible viscoelastic fluids having a differential constitutive law. The models considered here are Jeffreys' and Maxwell's. In both cases, we establish the existence of an asymptotic expansion in the neighbourhood of the steady incompressible fluid flow, with respect to the vanishing isothermal compressibility coefficient.

Existence locale et unicité d'ecoulements de fluides viscoélastiques dans des domaines non bornés C. R. Acad.Sci. Paris,t 328, Série I,pp.87-92 1999

In this Note, we present a result of local existence and uniqueness, for any initial data, of the solutions to the equations of viscoelastic fluids of Jeffreys type (differential constitutive law). The system of equations is supposed to be verified in an unbounded domain Ω ⊂ ℝN (N = 2 or 3)), uniformly regular. The difficulty comes essentially from the loss of compactness in the case of unbounded domains. To overcome this difficulty we use a local compactness method, which allows us to construct a sequence of solutions on subdomains ;inn whin which union covers Ω After that, we pass to the limit to define a solution over the whole domain. Finally we show the uniqueness of this solution in its class of regularity, by using an energy estimate

Existence results for steady flow of weakly compressible viscoelastic fluids with differential constituve law Differential &integral equations, vol 12,Nu 5,pp.741-772 1999

In this paper we study flows of viscoelastic weakly compressible fluids having a differential constitutive equation. In both cases, Jeffreys and Maxwell type constitutive equations, we establish a result of existence and uniqueness of solutions. We also show that, when the compressibility goes to zero, then the weakly compressible steady solution goes to the incompressible one

Unsteady flows of viscoelastic fluids with inflow and outflow boundary conditions Appl. Math,Lett., vol.9,Nu.5,p.93-98 1996

In this paper, we prove an existence and uniqueness result for unsteady flows of viscoelastic fluids through a strip with inflow and outflow boundary conditions, which can be regarded as perturbations of rigid motions. The fluids obey a constitutive law of Oldroyd type.

Ecoulements stationnaires de fluides viscoélastiques faiblement compressibles C.R. Acad.Sci. Paris, t.320, Serie I, p.1025-1030 1995

Nous considérons des écoulements stationnaires de fluides viscoélastiques faiblement compressibles. Les lois de comportement sont de type différentiel. Nous montrons, pour des forces extérieures petites, l'existence et l'unicité de solutions de modèles de types Jeffreys ou Maxwell. Puis nous concluons par la convergence de ces écoulements vers les écoulements incompressibles lorsque la compressibilité isothermique tend vers zéro

Supervision 11 Supervised Students
Regularized Oldroyd model: modeling and existence results

Lamis Marlyn Kenedy Ali Sabbagh
Master M2 Thesis: Partial Differential Equations and Numerical Analysis in 2015

Reaction diffusion equations and brain metabolism model

Hawraa Mohammad AlSayed
Master M2 Thesis: Partial Differential Equations and Numerical Analysis in 2016

Modélisation et analyse mathématique de modèles en océanographie

Ralf LTEIF
Dans cette thèse, nous nous intéressons au comportement d'un système composé de deux fluids non miscibles, soumis à la seule force de gravité. Un tel système est utilisé en océanographique, afin de modéliser une étendue d'eau de densités différentes. Récemment et dans la littérature plusieurs auteurs ont commencé par écrire sous forme "agréable" les equations d'évolution gouvernant le systême. Ensuite, ils ont developpé des modèles asymptotiques, dans les régimes d'eau peu profonde,on suppose que la profondeur des couches de fluides est petite devant la longueur d'onde caractéristique à l'interface, et d'ondes longues, oit l'on ajoute une hypothèse de petitesse des deformations a l' interface. Le but de cette thèse est de justifier rigoureusement et d'étudier mathématiquement plusieurs modèles utilisés en océanographic avec fond variable. Un travail de modélisation sera également envisagé pour la généralisation de modèles physiques existants appliqués à des situations plus réalistes. La première phase de la thèse consistera à analyser rigoureusement le modele d'ondes internes entre deux fluides de densités différentes afin de dériver des équations consistantes dans plusieurs régimes fortement non-linéaires et dispersifs et avec fond variable. 11 if existe pas A ce jour de justification rigoureuse (derivation, existence, unicite et stabilite de la solution) pour des nombreux modeles physiques decrivant cette situation (modele de Green-Naghdi/Green-Naghdi sous différents regimes). Un autre aspect de la these sera l'analyse mathematique (existence, unicite, stabi lite de Ia solution) de problemes environnetnentaux lies a ('oceanographie comme les modeles unidirectionnels fond variable et des simulations numeriques seront envisages. Pour cette these, une solidc formation en EDP est requise, et des connaissances en analyse numerique sont Ies bienvenues.

Analyse mathématique d’écoulements gravitaires visco-elasto-plastiques

Bilal ALTAKI

Nous nous intéresserons dans cette thèse aux équations régissant les écoulements de fluides visqueux incompressibles gravitaires à surface libre. Le but sera d'obtenir des résultats mathématiques et numériques probant autour de modèles récents de type visco-élasto-plastique. Des exemples en géophysiques de tels écoulements sont les mouvements de dunes de sable, les écoulements pyroclastiques, les glissements de terrain, les avalanches de neige. Dans un premier temps, nous travaillerons sur le livre de M. Fuchs et G. Seregin pour généraliser les résultats au cas non homogène avec un seuil de plasticité dépendant de la densité (On pourra également consulter le mémoire de M2R d'A. Berger). Nous essaierons ensuite de prendre en compte un critère de plasticité de type Drucker-Prager cad dépendant de la pression. La récente thèse de C. Lusso (CERMICS 2013) sera le point de départ. Finalement nous travaillerons sur la prise en compte du caractère visco-élasto-plastique sur la base des travaux développés par P. Saramito et al. Nous essaierons ensuite de généraliser les résultats au cas compressible : cadre naturel pour les écoulements de type Saint-Venant. On pourra s'appuyer sur les travaux récents de l'école Russe avec A. Mamontov, V. Shelukhin

Analyse mathématique des méthodes numériques stochastiques de la dynamique moléculaire

Houssam ALRACHID

In computational statistical mechanics, good sampling techniques are required to obtain macroscopic properties through averages over microscopic states. The main diff'culty is that these microscopic states are typically clustered around typical configurations, and a complete sampling of the configurational space is thus in general very complex to achieve. Techniques have been proposed to efficiently sample (i) the microscopic states and (ii) trajectories at the microscopic level. In the first case, one is interested in sampling a statistical ensemble, such as the canonical ensemble. An important example of quantities of interest in such a case is the free energy [4]. In the second case, one is interested in generating trajectories between typical configurations. The aim is for example to identify the transition states between two 'metastable configurations. In this PhD project, we would like to explore various techniques in both directions (i) and (ii). First, we would like to study two extensions of the classical adaptive biasing force technique [s]: (a) an extension using a projection of the force on a gradient, to reduce the variance and enhance the convergence and (b) an extension to deal with high-dimensional reaction coordinates, following a previous work [1]. Second, we will focus on recent results concerning accelerated dynamics methods that have been obtained for overdamped Langevin dynamics [2] and try to adapt them to Langevin dynamics (in the phase space).

Analyse mathématique et numérique de modèle de couplage chimiotaxie-fluide

Georges Chamoun

Modèles discrets de dislocations:ondes progressives et dynamique de particules

Mohamad AL HAJ

Etude mathématique de quelques EDP non linéaires modélisant la propagation d'ondes dans un milieu à la fois dispersif et dissipatif

Bassam Kojok

Etude mathématique de quelques problèmes issus de la mécanique des fluides viscoélastiques:écoulements dans des domaines singuliers

Zaynab salloum

Cette 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

Optimisation des bruits d'avion au voisinage des aéroports

Lina Abdallah

Languages
Arabic

Native or bilingual proficiency

English

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French

Native or bilingual proficiency