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Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
- Source :
- Mathematical Problems in Engineering, Vol 2015 (2015)
- Publication Year :
- 2015
- Publisher :
- Hindawi Limited, 2015.
-
Abstract
- Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equationutt-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.
- Subjects :
- Article Subject
Semigroup
lcsh:Mathematics
General Mathematics
Mathematical analysis
General Engineering
Absorbing set (random dynamical systems)
Moment of inertia
lcsh:QA1-939
Term (time)
Compact space
lcsh:TA1-2040
Attractor
Uniqueness
lcsh:Engineering (General). Civil engineering (General)
Beam (structure)
Mathematics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2015
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....367be5a5d43f572d8ae43f8f269057b4