Papers by Arij Bouzelmate
WSEAS TRANSACTIONS ON MATHEMATICS
HAL (Le Centre pour la Communication Scientifique Directe), Jun 27, 2022
Cet article étudie l'articulation entre aspects formels et aspects pédagogiques de l'outil vidéo ... more Cet article étudie l'articulation entre aspects formels et aspects pédagogiques de l'outil vidéo dans l'enseignement supérieur des mathématiques. S'appuyant sur des vidéos réalisées par les auteurs sur les équations différentielles ordinaires, il s'intéresse à l'outil en tant qu'élément d'un Espace de Travail Mathématique.
Cornell University - arXiv, Dec 2, 2022
This article presents some technical and pedagogical considerations about a series of videos made... more This article presents some technical and pedagogical considerations about a series of videos made by the authors to teach elementary theory of differential equations. Intended to be a pedagogical support for undergraduate students of scientific curricula, these videos provide rigorous mathematical contents in a form that takes into account the specificities of the tool. Videos for teaching mathematics should be seen as a specific way for providing rigorous scientific content to learners, and should not be reduced to oral manuals or standard classroom lessons. Research Contribution: Arij Bouzelmate and Benoît Rittaud are searcher and teacher in mathematics. Arij Bouzelmate is a specialist in partial differential equations and director of LaR2A. Benoît Rittaud is a specialist in discrete mathematics and is involved in popularization of mathematics.
Nonlinear functional analysis and applications, May 23, 2021
Abstract. This paper concerns the existence, uniqueness and asymptotic properties (as r = |x | → ... more Abstract. This paper concerns the existence, uniqueness and asymptotic properties (as r = |x | → ∞) of radial self-similar solutions to the nonlinear Ornstein-Uhlenbeck equation vt = ∆pv + x · ∇(|v | q−1 v) in R N × (0, +∞). Here q> p − 1> 1, N ≥ 1, and ∆p denotes the p-Laplacian operator. These solutions are of the form v(x, t) = t −γ U(cxt −σ), where γ and σ are fixed powers given by the invariance properties of differential equation, while U is a radial function, U(y) = u(r), r = |y|. With the choice c = (q − 1) −1/p, the radial profile u satisfies the nonlinear ordinary differential equation (|u ′ | p−2 u ′ ) ′ +
In this paper, we study existence and uniqueness of radial solutions for the degenerate elliptic ... more In this paper, we study existence and uniqueness of radial solutions for the degenerate elliptic equation Δ p U + α x • ∇U + β x • ∇(|U | q−1 U) + U = 0 in IR N where p > q+1 > 2, N ≥ 1, α ∈ IR, β ≤ 0. We give also a classification of solutions and the behaviour of those which are positive.
International Journal of Mathematical Analysis, 2015
We study the existence and asymptotic behavior near the origin of radial entire solutions of the ... more We study the existence and asymptotic behavior near the origin of radial entire solutions of the singular elliptic equation ∆ p U + αU + βx • ∇U + |x| l |U | q−1 U = 0 in IR N where p > 2, q ≥ 1, N ≥ 1, α < 0, β < 0 and l < 0. The behavior and the existence of positive solutions depends strongly on the sign of (N − p) l + p(N − 1) p − 1 .
WSEAS TRANSACTIONS ON MATHEMATICS
Our purpose is to give existence results of decaying solutions of the above equation and their as... more Our purpose is to give existence results of decaying solutions of the above equation and their asymptotic behavior near infinity. The study depends 1 q+1−p r −p q+1−p .
This paper concerns the existence, uniqueness and asymptotic properties (as r = |x| ! 1) of radia... more This paper concerns the existence, uniqueness and asymptotic properties (as r = |x| ! 1) of radial self-similar solutions to the nonlinear Ornstein-Uhlenbeck equation vt = pv + x · r(|v| q 1 v) in R N ◊(0,+1). Here q > p 1 > 1, N 1, and p denotes the p-Laplacian operator. These solutions are of the form v(x,t) = t U(cxt ), where and are fixed powers given by the invariance properties of dierential equation, while U is a radial function, U(y) = u(r), r = |y|. With the choice c = (q 1) 1/p , the radial profile u satisfies the nonlinear ordinary dierential equation (|u 0 | p 2 u 0 ) 0 + N 1 r |u 0 | p 2 u 0 + q + 1 p p ru 0 + (q 1)r(|u| q 1 u) 0 + u = 0 in R+. We carry out a careful analysis of this equation and deduce the corre- sponding consequences for the Ornstein-Uhlenbeck equation.
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Papers by Arij Bouzelmate