Global attractors for the suspension bridge equations with nonlinear damping

Abstract

Abstract. In this paper, we prove the existence of a global attractor for the suspension bridge equations with nonlinear damping.

Random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type

“…If we ignore the effects of white noises in (1.1), that is, q B (x) ≡ q S (x) ≡ 0, then there are a lot of profound results on the dynamics of a variety of deterministic systems related to (1.1), see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the reference therein. For example, just for a single deterministic suspension bridge equation (without white noises), in [3][4][5][6][7][8][9]18], the authors investigated the existence, uniqueness, and global attractors of the solution. And for the deterministic coupled string-beam equations (without white noises) and the similar problems, Woinowsky-Krieger gave existence and uniqueness of the solution in the different spaces [17].…”

Long-time behavior of a suspension bridge equations with past history

“…The suspension bridge equations were presented by Lazer and McKenna as new problems in the field of nonlinear analysis [12]. The global existence and the global attractors of solutions for the suspension bridge equation were studied in [1,2,[14][15][16]18,20,22] and references therein. Ma and Zhong [15] investigated the existence of global attractors of the weak solutions for the suspension bridge equations.…”

“…Zhong et al [22] proved the existence of strong solutions and global attractors for the suspension bridge equations. Park and Kang [18,20] obtained the existence of pullback attractor for the non-autonomous suspension bridge equations and the existence of global attractors for the suspension bridge equations with nonlinear damping, respectively. For the coupled suspension bridge equations, Ahmed and Harbi [1] studied the existence of weak solution.…”

Global attractor for suspension bridge equations with memory

“…The suspension bridge equations were presented by Lazer and McKenna as new problems in the field of nonlinear analysis . The global existence and the global attractors of solutions for the suspension bridge equation were studied in and references therein. An proved the existence and uniqueness of a weak solution for k >− 1 and then proved decay estimates of the solution for the suspension bridge equation.…”

“… obtained the existence of strong solutions and global attractors for the suspension bridge equations. Park and Kang investigated the existence of pullback attractor for the non‐autonomous suspension bridge equations and the existence of global attractors for the suspension bridge equations with nonlinear damping, respectively. However, the existence of global attractors for the suspension bridge equation with memory was no yet considered.…”