Lp-boundedness and topological structure of solutions for flexible structural systems

This work deals with L-p-boundedness of mild solutions for an abstract version of the damped wave equation u '' +alpha u ''' =beta Delta u + gamma Delta u' +f that models the vibrations of flexible structures possessing internal material damping and external force f. We prove that the set consisting ofmild 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 (C) 2015 JohnWiley & Sons, Ltd.