Exploring Thermoelastic Effects in Damped Bresse Systems with Distributed Delay

In this work, we consider the one-dimensional thermoelastic Bresse system by addressing the aspects of nonlinear damping and distributed delay term acting on the first and the second equations. We prove a stability result without the common assumption regarding wave speeds under Neumann boundary conditions. We discover a new relationship between the decay rate of the solution and the growth of ϖ at infinity. Our results were achieved using the multiplier method and the perturbed modified energy, named Lyapunov functions together with some properties of convex functions.

• nonlinear damping
• distributed delay
• stability
• decay rate
• Neumann boundary conditions
• Lyapunov function
• convex functions
• augmented Lagrangian method

• Stability and Controllability of Differential Equations
• Thermoelastic and Magnetoelastic Phenomena
• Vibration and Dynamic Analysis
• nonlinear damping
• distributed delay
• stability
• decay rate
• Neumann boundary conditions
• Lyapunov function
• convex functions
• augmented Lagrangian method
• Control and Systems Engineering
• Mechanics of Materials
• Engineering