Well-posedness and stability for Bresse-Timoshenko type systems with thermodiffusion effects and nonlinear damping

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.

• well-posedness
• global existence and uniqueness
• nonlinear damping
• thermal diffusion
• mass diffusion
• thermoelastic effect
• exponential stability
• polynomial decay rate
• Lyapunov function
• augmented Lagrangian method

• Stability and Controllability of Differential Equations
• Thermoelastic and Magnetoelastic Phenomena
• Vibration and Dynamic Analysis
• well-posedness
• global existence and uniqueness
• nonlinear damping
• thermal diffusion
• mass diffusion
• thermoelastic effect
• exponential stability
• polynomial decay rate
• Control and Systems Engineering
• Mechanics of Materials
• Engineering