Well-posedness and stability for bresse-timoshenko type systems with thermodiffusion effects and nonlinear damping

Abstract

Nonlinear Bresse-Timoshenko beam model with thermal, mass diffusion and theormoelastic effects is studied. We state and prove the well-posedness of problem. The global existence and uniqueness of solution is proved by using the classical Faedo-Galerkin approximations along with two a priori estimates. We prove an exponential stability estimate under assumption (2.3)1 and polynomial decay rate for solution under (2.3)2, by using a multiplier technique combined with an appropriate Lyapuniv functions.