Mathématiques

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Browsing Mathématiques by Subject "Existence, uniqueness"

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    Existence, uniqueness and asymptotic behavior of solution
    (20 August 1955 university of Skikda, 2024) Boughamsa. Wissem; Amar ,OUAOUA
    In this thesis, we study the various problems of nonlinear wave equations with source terms and variable coefficients, sometimes with damping and sometimes with viscoelastic terms, under suitable assumptions on variable coefficients. At the beginning, we presented a series of summaries of some previous works by several researchers and the results they have obtained. We have studied several results. In the first problem, we proved the existence and uniqueness of the solution, and then we proved that the solution blows up in finite time. To verify our theoretical results, we conducted some numerical tests in the form of figures, and their results matched the theoretical analytical study. As for the second problem, we proved the existence and uniqueness of the solution and showed its global existence in the presence of positive initial energy, also demonstrated energy decay when time is sufficiently large, we relied on the Nehari space. The third problem, we proved blow-up in finite time in the both the analytical and numerical results of the solution. In the forth problem, we proved the existence of a local solution and also proved that the local solution is global. Finally, stability of the solution was obtained using a very important result known as the Komornik’s condition, and a numerical example was given to illustrate the result, which also matched the analytical results. In fact, Galerkin-Faedo approximations and fixed point theory were used to establish the existence and uniqueness of the solution. At the end of the thesis, we provided a conclusion and perspectives