Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges-Reference-Cited by-同舟云学术

Global attractors for a nonlinear plate equation modeling the oscillations of suspension bridges

Published:2023 Issue:3 Volume:15 Page:436-456
ISSN:2836-3310
Container-title:Communications in Analysis and Mechanics
language:
Short-container-title:CAM

Author:

Liu Yang¹²

Affiliation:

1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China

2. College of Mathematics, Sichuan University, Chengdu 610065, China

Abstract

<abstract><p>This paper is concerned with a nonlinear plate equation modeling the oscillations of suspension bridges. Under mixed boundary conditions consisting of simply supported and free boundary conditions, we obtain the global well-posedness of solutions in suitable function spaces. In addition, we use the perturbed energy method to prove the existence of a bounded absorbing set and establish a stabilizability estimate. Then, we derive the existence of a global attractor by verifying the asymptotic smoothness of the corresponding dissipative dynamical system.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference36 articles.

1. R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.

2. M. Al-Gwaiz, V. Benci, F. Gazzola, Bending and stretching energies in a rectangular plate modeling suspension bridges, Nonlinear Anal., 106 (2014), 18–34. https://doi.org/10.1016/j.na.2014.04.011

3. G. Arioli, F. Gazzola, A new mathematical explanation of what triggered the catastrophic torsional mode of the Tacoma Narrows Bridge, Appl. Math. Model., 39 (2015), 901–912. https://doi.org/10.1016/j.apm.2014.06.022

4. U. Battisti, E. Berchio, A. Ferrero, F. Gazzola, Energy transfer between modes in a nonlinear beam equation, J. Math. Pures Appl., 108 (2017), 885–917. https://doi.org/10.1016/j.matpur.2017.05.010

5. E. Berchio, A. Ferrero, F. Gazzola, Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions, Nonlinear Anal. Real World Appl., 28 (2016), 91–125. https://doi.org/10.1016/j.nonrwa.2015.09.005

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