Achour, HossemddineAdvisor: Sengouga, A.2023-05-112023-05-112016-06-10https://repository.univ-msila.dz/handle/123456789/37957This work is devoted to the study the asymptotic behavior in time Ofa vibrating string With afixed end-point and the other is a moving one. Using the multiplier method (energy integrals) we show that the energy ofthe string decay in time. We have considered both cases ofwaves With constant and variable speed and different motions ofthe variable end-point. Moreover some numerical results are obtained using the penalization method.enwave equation, non-cylindrical domains, multiplier method, penalization.Thesis