Doctorat (Mathématiques)
http://depot.umc.edu.dz/handle/123456789/8691
Wed, 28 Sep 2022 19:31:22 GMT2022-09-28T19:31:22ZContributions aux problèmes variationnels et aux inclusions différentielles dans les espaces de Banach.
http://depot.umc.edu.dz/handle/123456789/8905
Contributions aux problèmes variationnels et aux inclusions différentielles dans les espaces de Banach.
Bounekhel, Djalal; Kechkar, Nasserdine
The thesis consists in three chapters. In the first one, we state all needed definitions and concepts
and some preliminary results. In Chapter 2, we study the existence of solutions for nonconvex
quasi-variational problems in smooth reflexive Banach spaces. The third chapter is devoted to the
study of existence of solutions for nonconvex state dependent sweeping processes in smooth
reflexive Banach spaces. At the end of the thesis, we state a conclusion of all obtained results
together with a list of some open problems that may interest the researchers in the field.
Wed, 03 Nov 2021 00:00:00 GMThttp://depot.umc.edu.dz/handle/123456789/89052021-11-03T00:00:00ZNombre de cycles limites des systèmes différentiels polynômiaux perturbés à centres linéaires.
http://depot.umc.edu.dz/handle/123456789/8904
Nombre de cycles limites des systèmes différentiels polynômiaux perturbés à centres linéaires.
Debz, Nassima; Berkane, Abdelhak; Boulfoul, Amel
In this thesis we study the limit cycles of two classes of ordinary differential syst`ems depending of small parameter. Using a theorem of first and second order averaging theory we transform the study of limit cycles of ordinary differential systems to the study of non-degenerate zeros of an algebraic systems. The first class deals with the generalized polynomial differential system of the form :
x ˙ = y − ε(g11(x) + f11(x)y) − ε2(g12(x) + f12(x)y),
y ˙ = −x − ε(g21(x) + f21(x)y − p1(x)y2 − q1(x)y3)
− ε2(g22(x) + f22(x)y − p2(x)y2 − q2(x)y3),
where fi,j, gi,j (1 ≤ i, j ≤ 2) and pi, qi (1 ≤ i ≤ 2) are polynomials of given degree.
The second class is studied the generalized polynomial Kukles differential
system of the form :
x ˙ = −y + εl1(x) y2α + ε2l2(x) y2α,
y ˙ = x − ε f1(x) y2α + g1(x) y2α+1 + h1(x) y2α+2 + d1 0 y2α+3 ,
+ ε2 f2(x) y2α + g2(x) y2α+1 + h2(x) y2α+2 + d2 0 y2α+3 ,
where fi(x), gi(x), hi(x) and li(x), (1 ≤ i ≤ 2) are polynomials of given degree,
di
0 6= 0, (1 ≤ i ≤ 2), α ∈ N and ε is a small parameter. This study is illustrated by examples .
Thu, 03 Feb 2022 00:00:00 GMThttp://depot.umc.edu.dz/handle/123456789/89042022-02-03T00:00:00ZAutour des méthodes spectrales pour la résolution des équations aux dérivées partielles.
http://depot.umc.edu.dz/handle/123456789/8903
Autour des méthodes spectrales pour la résolution des équations aux dérivées partielles.
Lateli, Ahcene; Hamaizia, Tayeb; Boutagou, Amor
This thesis consists of four distinct but complementary chapters. The first chapter contains, on the one hand, some to reminders on Sobolev spaces and polynomial spaces with their associated norms, which constitute the framework of the numerical analysis of spectral methods and, on the other hand, it devotes to the reminders on orthogonal polynomials without and with weights and their main properties, and introduces some associated transformations where orthogonal polynomials are widely used in approximation theory. The second chapter exposes in a clear and elegant the forms of Gaussian quadrature, Gauss-Lobatto quadrature formula and weighted formula and the study of some estimates. These quadrature formulas are considered to constriction of numerical quadrature formulas of high precision. In the third chapter is the study of the approximation of the differential problem by the spectral method, wich is a technique for approximating solutions of partial differential equations. Their main characteristics are that the discrete solutions are sought in high degree polynomial spaces. The discretization is then performed by replacing the space of test functions by a space of polynomials and by calculating the integrals by means of appropriate quadrature formulas. The quadrature formula used is the Gauss-Lobatto-Legendre formula applied in the x direction. This method is equivalent to a collocation method. We see that the error decreases exponentially when the discretization parameter N becomes large. The purpose of the fourth chapter is to develop a spectral method to solve the given problem using the matrixs; to convert the differential problem in a system of ordinary differential equations easier to solve or a linear system; to explain how the discrete problem identified in the Chapter Three can be implemented on computer; to study the behaviour of condition numbers; to solve the linear system and give a graphic illustration in the case of explicit and implicit solutions. Programming is done by Maple.
Thu, 27 Jan 2022 00:00:00 GMThttp://depot.umc.edu.dz/handle/123456789/89032022-01-27T00:00:00ZSynchronisation et contrôle dans les systèmes dynamiques.
http://depot.umc.edu.dz/handle/123456789/8902
Synchronisation et contrôle dans les systèmes dynamiques.
Zarour, Abdelwahab; Latrous, Chahla; Ouannas, Adel
This paper is concerned with the topic of chaos control in fractional maps. It presents two linear control laws to stabilize the dynamics of a new three-dimensional fractional Henon map. The chaos control has been achieved by proving a new theorem,based on a suitable Lyapunov function and a linear method. Finally, numerical simulations have been carried out to highlight the e_ectiveness of the proposed control method.
Mon, 19 Jul 2021 00:00:00 GMThttp://depot.umc.edu.dz/handle/123456789/89022021-07-19T00:00:00Z