Abstract
This work deals with Lp‐boundedness of mild solutions for an abstract version of the damped wave equation u′′+αu′′′=βΔu + γΔu′+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.
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