Well-Posedness and Existence of Global and Exponential Attractors for a Nonlinear Model of a Bresse-Type Deck Bridge

Abstract This study examines the well-posedness and asymptotic behavior of a nonlinear suspension bridge with a deck modeled according to the Bresse vibration theory. We establish the existence and uniqueness of global solutions by means of semigroup theory of linear operators, which gives rise to a dynamical system of solutions. From the perspective of quasi-stability properties, we prove the existence of a global and exponential attractor for the dynamical system and the finiteness of the fractal dimension and the regularity of the attractor. Finally, we establish conditions for a finite set of bounded linear functionals defined on phase space to be a set of determining functionals for the dynamical system.