Département mathématique et informatique

Permanent URI for this collectionhttps://dspacee.univ-temouchent.edu.dz/handle/123456789/697

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    Blow-Up Result for a Class of Wave p-Laplace Equation with Nonlinear Dissipation in R^n
    (Vladikavkaz Mathematical Journal, 2021-03-01) BENIANI, ABDERRAHMANE
    The Laplace equations has been studied in several stages and has gradually developed over the past decades. Beginning with the well-known standard equation ∆u = 0, where it has been well studied in all aspects, many results have been found and improved in an excellent manner. Passing to p-Laplace equation ∆pu = 0 with a constant parameter, whether in stationary or evolutionary systems, where it experienced unprecedented development and was studied in almost exhaustively. In this article, we consider initial value problem for nonlinear wave equation containing the p-Laplacian operator. We prove that a class of solutions with negative initial energy blows up in finite time if p > r > m, by using contradiction argument. Additional difficulties due to the constant exponents in Rn are treated in order to obtain the main conclusion. We used a contradiction argument to obtain a condition on initial data such that the solution extinct at finite time. In the absence of the density function, our system reduces to the nonlinear damped wave equation, it has been extensively studied by many mathematicians in bounded domain.
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    Well-posedness and general energy decay of solution for transmission problem with weakly nonlinear dissipative
    (Journal of Integral Equations and Applications, 2021-08-31) BENIANI, ABDERRAHMANE
    In this paper, we consider a transmission problem in a bounded domain with a nonlinear dissipation in the first equation. Under suitable assumptions on the weight of the damping, we show the existence and uniqueness of solution by the Faedo–Galerkin method. Also we prove general stability estimates using some properties of convex functions and Lyaponov functional.
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    Stability for Weakly Coupled Wave Equations with a General Internal Control of Diffusive Type
    (Axioms Mathematics, 2023-01-02) BENIANI, ABDERRAHMANE
    The present paper deals with well-posedness and asymptotic stability for weakly coupled wave equations with a more general internal control of diffusive type. Owing to the semigroup theory of linear operator, the well-posedness of system is proved. Furthermore, we show a general decay rate result. The method is based on the frequency domain approach combined with multiplier technique
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    Decay Properties for Transmission System with Infinite Memory and Distributed Delay
    (Fractal and Fractional, 2024-12-31) BENIANI, ABDERRAHMANE
    We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional
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    Polynomial Decay of the Energy of Solutions of the Timoshenko System with Two Boundary Fractional Dissipations
    (Fractal and Fractional, 2024-08-28) BENIANI, ABDERRAHMANE
    In this study, we examine Timoshenko systems with boundary conditions featuring two types of fractional dissipations. By applying semigroup theory, we demonstrate the existence and uniqueness of solutions. Our analysis shows that while the system exhibits strong stability, it does not achieve uniform stability. Consequently, we derive a polynomial decay rate for the system.
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    ON BOUNDARY VALUE PROBLEMS WITH IMPLICIT RANDOM NON-CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS
    (SARAJEVO JOURNAL OF MATHEMATICS, 2023) BEKADA, FOUZIA; ABDELKRIM, SALIM
    In this paper, we present some results on the existence, uniqueness and Ulam stability for a class of problems for nonlinear implicit random fractional differential equations with non-conformable derivatives. For our proofs, we employ some suitable fixed point theorems. Finally, we provide some illustrative examples.
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    Dynamics and stability for Katugampola random fractional differential equations
    (AIMS Mathematics, 2021) Bekada, Fouzia; Abbas, Saıd; Benchohra, Mouffak; Nieto, Juan J
    This paper deals with some existence of random solutions and the Ulam stability for a class of Katugampola random fractional differential equations in Banach spaces. A random fixed point theorem is used for the existence of random solutions, and we prove that our problem is generalized Ulam-Hyers-Rassias stable. An illustrative example is presented in the last section.
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    Boundary Value Problem for Caputo–Fabrizio Random Fractional Differential Equations
    (2020) Bekada, Fouzia; Abbas, Said
    This article deals with some existence of random solutions and Ulam stability results for a class of Caputo-Fabrizio random fractional differential equations with boundary conditions in Banach spaces. Our results are based on the fixed point theory and random operators. Two illustrative examples are presented in the last section