2015/11/20 by To Fu Ma, Ma, To Fu, Rodrigo Nunes Monteiro +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #35B41 #35L53 #74K10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1511.06786
openalex publication_date 2015/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Bresse system is a valid model for arched beams which reduces to the classical Timoshenko system when the arch curvature ℓ=0. Our first result shows the Timoshenko system as a singular limit of the Bresse system as ℓ → 0. The remaining results are concerned with the long-time dynamics of Bresse systems. In a general framework, allowing nonlinear damping and forcing terms, we prove the existence of a smooth global attractor with finite fractal dimension and exponential attractors as well. We also compare the Bresse system with the Timoshenko system, in the sense of upper semicontinuity of their attractors as ℓ → 0.