Thème :
Stability, numerical study of hyperbolic partial differential equation
Présentation :
we consider a one dimensional Bresse-Timoshenko beam model with microtemperature effect and viscous damping acting on the transverse displacement of the beam. We state and prove the global well-posedness of the problem by using the Faedo-Galerkin approximations along with some a priori estimates. We construct a suitable Lyapunov functional based on the multipliers method and we show that the energy decays in exponential manner irrespective on the wave speeds of the system or any other conditions on the system parameters. Finally, we present some numerical tests to illustrate the theoretical results by carrying out an Euler scheme for time discretization and the classical finite difference method for the spatial discretization.