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Avancées en Mathématiques Pures et Appliquées


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[Forthcoming] Régions invariantes et existence globale de solutions pour un système de réaction-diffusion généralisé à m-composants avec une matrice de diffusion tridiagonale de Toeplitz symétrique

The aim of this paper is to construct invariant regions of a generalized m-component reaction-diffusion system with tridiagonal symmetric Toeplitz diffusion matrix and nonhomogeneous boundary conditions and polynomial growth for the nonlinear reaction terms. Using the eigenvalues and eigenvectors of the diffusion matrix and the parabolicity conditions. So we prove the global existence of solutions using Lyapunov functional.


[Forthcoming] Les opérateurs maximaux dans les espaces de Dunkle-Fofana

We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.


[Forthcoming] Estimations à priori pour l’équation elliptique super-linéaire : le problème de la valeur au bord de Neumann

We study in this paper the nonexistence of finite Morse index solutions of some Neumann boundary value problems.


[Forthcoming] Déficience D’une Onde Viscoélastique Non Linéaire : Équation Avec Dissipation Aux Limites

In this work we establish a general decay rate for a nonlinear viscoelastic wave equation with boundary dissipation where the relaxation function satis-es g’ (t) ≤ – ξ (t) g p (t) , t ≥ t 0, 1 ≤ p ≤ 32. This work generalizes and improves earlier results in the literature.


[Forthcoming] Problème de la valeur initiale pour le système dynamique des gaz à pression nulle non conservateur

In this article, we study initial value problem for the zero-pressure gas dynamics system in non conservative form and the associated adhesion approximation. We use adhesion approximation and modi-ed adhesion approximation in the construction of weak asymptotic solution. First we prove a general existence result for the adhesion model for the initial velocity component in Hs for s > (n2) + 1 and the initial data for the density component being a C1 function. Using this, we construct weak asymptotic solution for the system with initial velocity in L2 ∩ L and the initial density being a bounded Borel measure. Then we make a detailed analysis of the explicit formula for the weak asymptotic solution and generalized solution for the plane-wave type initial data.


[Forthcoming] Multiplicité de solutions pour un problème non homogène impliquant un potentiel dans les espaces d’Orlicz-Sobolev

This paper is devoted to the study of the nonhomogeneous problem –div(a(|∇u|)∇u) + a(|u|)u = λV (x)|u|m(x)-2u – μg(x,u) in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in ℝN, λ, μ are positive real numbers, V (x) is a potential, m : Ω → (1, ∞) is a continuous function, a is mapping such that ϕ(|t|)t is increasing homeomorphism from ℝ to ℝ and g : Ω × ℝ → ℝ is a continuous function. We establish there main results with various assumptions, the first one asserts that any λ > 0 is an eigenvalue of our problem. The second Theorem states the existence of a constant λ* such that every λ ∈ (0, λ*) is an eigenvalue of the problem. While the third Theorem claims the existence of a constant λ** such that every λ ∈ [λ**, ∞} is an eigenvalue of the problem. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces.


[Forthcoming] Sur l’existence de solutions d’un problème biharmonique non local

This paper is concerned with the existence of an eigenvalue for a p(x)-biharmonic Kirchhoff problem with Navier boundary condition. Under some suitable conditions, we establish that any λ > 0 is an eigenvalue . The proofs combine variational methods with energy estimates. The main results of this paper improve and generalize the previous one introduced by Kefi and Rădulescu (Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), 439-463).


Autres numéros :

2020

Volume 20- 11

Numéro 1 (Mai 2020)
Numéro 2 (Septembre 2020)

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