Lp‐boundedness and topological structure of solutions for flexible structural systems. (26th February 2015)

• Record Type: Journal Article
• Authors: Andrade, Filipe; Cuevas, Claudio; Dantas, Filipe; Soto, Herme
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 18(2015:Dec. 15)
• Page Start: 5139
• Page End: 5159
• Publication Date: 2015-02-26
• Subjects: Flexible structure -- Kneser's property -- Mild solutions -- Regularized families; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3439
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This work deals with L p ‐boundedness of mild solutions for an abstract version of the damped wave equation u ′′ + α u ′′′ = β Δ u + γ Δ u ′+ f that models the vibrations of flexible structures possessing internal material damping and external force f. We prove that the set consisting of mild solutions for this problem is compact and connected in the space of continuous functions. This property is known in the literature as the Kneser's property. Copyright © 2015 John Wiley & Sons, Ltd.