Browsing by Author "OUAOUA , Amar"

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    ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A PARTIAL DIFFERENTIAL EQUATION
    (Faculty of Sciences, 2024) Aiachi , Marwa; OUAOUA , Amar
    In this memory, we study two problems: the first concerns a quasi-linear parabolic system with a weak visco-elastic term, and the second concerns the wave equation. In the first problem, we proved the existence of a global solution in a bounded domain with homogeneous Dirichlet conditions. We also proved that this solution decays exponentially, meaning that as time approaches to infinity, the solution approaches to zero. Second, we proved that the solution to the wave equation, also under homogeneous Dirichlet conditions, blows up in finite time. The study is based on Nehari space.
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    Stability of solution for a class of wave equation : Analytical results
    (Faculty of sciences, 2023) Bouzitouna , Selma; Boucenna , Linda; OUAOUA , Amar
    In the first chapter of memory, we present a variety of important partial differential equations, which include the following types of equations : elliptic, parabolic, and hyperbolic equations. We also write down the formal form of each type of equation. In the second chapter, we present important theories and deffnitions, and we also study the asymptotic behavior pectific type of hyperbolic partial defferential eqations of the kirchhoff-type, using the energy method, with the homogeneous Dirichlet boundary conditions. We then prove that the solution is global and stable under two cases: frstly, stability is achived through an expenential function where the energy dissipates as it goes to infinity, and secondly, stability is in the form of a pawer function. In the final chapter, we repeat the previous work by replacing the exponential constants with exponential variables, resulting in the same outcomes