Energy decay and blow-up of solutions for a coupled suspension bridge model with nonlinear dampings

In this paper, a coupled suspension bridge model with nonlinear dampings and sources is investigated. By the potential well method, the global existence of potential well solutions is established. Polynomial decay rates of the total energy is obtained by combining the multiplier method with a weighted integral inequality. For the three cases that the initial total energy is negative, positive but small, and arbitrarily high, the blow-up results for weak solutions if the source terms are stronger than damping terms are discussed according to the differential inequality technique. These results improve and extend the recent works obtained by Ding and Zhou (Discrete Contin. Dyn. Syst. Ser. B 29(1)(2024): 550–572), which only discuss the linear dampings.