Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
Joint Authors
Wang, Danxia
Zhang, Sufang
Wang, Yinzhu
Zhang, Jianwen
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-02-22
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux)2dx)uxx-ϕ(∫0l(ux)2dx)uxxt=q(x), in [0,L]×R+ with the structural damping and the rotational inertia term.
Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions.
In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup.
In addition, the same results also can be proved under the other nonlinear boundary conditions.
American Psychological Association (APA)
Wang, Danxia& Zhang, Jianwen& Wang, Yinzhu& Zhang, Sufang. 2015. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074909
Modern Language Association (MLA)
Wang, Danxia…[et al.]. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions. Mathematical Problems in Engineering No. 2015 (2015), pp.1-10.
https://search.emarefa.net/detail/BIM-1074909
American Medical Association (AMA)
Wang, Danxia& Zhang, Jianwen& Wang, Yinzhu& Zhang, Sufang. Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074909
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074909