CERAMATHS - DMATHS seminar: presentation by Wafa Ahmedi

The CERAMATHS mathematics department seminar will welcome Wafa Ahmedi (ESSTH Sousse) at 2pm on Thursday, October 17, 2024, for the following talk:

Some results on the stabilization of a local systems with Kelvin-Voigt dampings

In this talk, first, we investigate the stabilization of locally transmission problems of two wave systems. We proved the strong stability by using Arendt and Batty criteria. Further, using a frequency domain approach combined with a multiplier technique, we established the exponential stability of the solution if and only if the waves of the second coupled equations have the same speed propagation (i.e., a₂ = 1). In the case a₂ \neq 1, we proved that the energy of our problem decays polynomially with the rate t^-1. Second, we study the stabilization of locally coupled wave-Euler Bernoulli beam equations with local Kelvin-Voigt dampings. We considered three cases: The case when the supports of the dampings and the coupling coefficients are disjoint and in the second and the third cases, we assume that there is an intersection between the damping and coupling regions. We proved a polynomial energy decay rate of type t^-1and t^-1/2. Next, we generalize this work to a multidimensional case and we study the strong stability of the system under several geometric conditions. Also, we showed that the corresponding semigroup is analytic when the Kelvin-Voigt dampings are globally distributed. Then, using one or two damping(s), we established an energy decay rate depending on the exponential or polynomial decay rate of two auxiliary problems.