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Exponential decay for elastic systems with structural damping and infinite delay. (English) Zbl 1432.34094

Summary: In this paper, we consider nonlinear evolution equations of second order in Banach spaces involving unbounded delay, which can model an elastic system with structural damping involving infinite delays. By using fixed point for condensing maps, we prove the existence and exponential decay of mild solutions. The obtained results can be applied to the nonlinear vibration equation of elastic beams with structural damping and infinite delay.

MSC:

34K20 Stability theory of functional-differential equations
47H08 Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc.
47H10 Fixed-point theorems
34K10 Boundary value problems for functional-differential equations
47N20 Applications of operator theory to differential and integral equations
35R10 Partial functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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