Abstract
We study the existence of pseudo S$S$-asymptotically ?$\omega$-periodic mild solutions for an abstract version of the damped wave equation u?+?u?=βΔu+?Δu?+f$u''+\alpha u'''=\beta\Delta u +\gamma\Delta u'+f$ which model the vibrations of flexible structures possessing internal material damping and external force f$f$. We show concrete applications of our methods to flexible structures, heat conduction, fractional equations and viscoelasticity.
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