Theoretical and numerical study of some models in mechanics

Abstract

n this dissertation, we study the existence and the long-term behavior of certain systems influ- enced by various dissipation mechanisms, damping effects, and delayed term. By imposing appropriate assumptions, we establish the well-posedness by the application of semigroup theory or the Faedo- Galerkin approach. To achieve the desired stability results for the systems, we employ the multiplier method. To support the theoretical findings, a numerical analysis is conducted for each problem. Fully dis- crete approximations are formulated using the finite-element method combined with the implicit Euler scheme. Numerical simulations, implemented in MATLAB, are provided to illustrate the accuracy of the approximations and the behavior of the solutions.