Araya, Daniela; Lizama, Carlos Existence of asymptotically almost automorphic solutions for a third order differential equation. (English) Zbl 1340.43003 Electron. J. Qual. Theory Differ. Equ. 2012, Paper No. 53, 20 p. (2012). Summary: This paper deals with results on existence of asymptotically almost automorphic solutions for a third order in time abstract differential equation which model, on one side, high intensity ultrasound in acoustic wave propagation, while on the other side, vibrations of flexible structures possessing internal material damping. We established the asymptotically almost automorphy of the output solution subject to the asymptotically almost automorphy of the input disturbance. Cited in 4 Documents MSC: 43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions 74D05 Linear constitutive equations for materials with memory 35P05 General topics in linear spectral theory for PDEs 47F05 General theory of partial differential operators 34G20 Nonlinear differential equations in abstract spaces Keywords:third order differential equation; asymptotically almost automorphic function; regularized families of bounded operators PDFBibTeX XMLCite \textit{D. Araya} and \textit{C. Lizama}, Electron. J. Qual. Theory Differ. Equ. 2012, Paper No. 53, 20 p. (2012; Zbl 1340.43003) Full Text: DOI