Departement de Mathématique

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Existence of the solution and stability of an evolution problem
(Université Oran 1, 2025-09-15) ALLALI Mohammed
This thesis is focus to studying the nonlinear Korteweg-de Vries equation with internal feedback without delay, also the boundary feedback with either constant or time-dependent delay. We prove the well-posedness of the system and establish the exponential stability of the equation using Lyapunov functional, under certain assumptions like the spatial domain length,also feedback mechanisms, and time-dependent delay. Also, we study the Korteweg-de Vries equation with internal time-varying delay feedback, by proving the exponential stability of the system using an appropriate Lyapunov functional without any assumptions on length of the spatial domain. Finally, we present numerical simulations to illustrate the obtained stability results.