Stabilisation des solutions pour certains problèmes d’ondes viscoélastiques et d’une plaque viscoélastique

Abstract

The main objective of this thesis is to study the stabilization of solutions for certain viscoelastic wave and plate problems, particularly the viscoelastic Euler-Bernoulli equation with a logarithmic nonlinear source. We focus on the asymptotic behavior of the solutions, specifically the decay of solutions under boundary control conditions of memory type. The method used relies on the analysis of multipliers and the properties of convex functions, leading to general decay results for the solutions. These results provide a deeper understanding of the stabilization phenomena for these viscoelastic problems and open new perspectives for their analysis in a bounded domain.