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Existence of asymptotically almost automorphic solutions for a third order differential equation. (English) Zbl 1340.43003

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.

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
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