We consider a family of nonautonomous viscoelastic equation with memory and singularly oscillating external forcing, together with the averaged equation.Under suitable assumptions on the nonlinearity and on the external force, the related solution processes acting on the natural weak energy space H are shown to possess uniform attractors Aµ. The family Aµ turns out to be bounded in H, uniformly with respect to the parameters involved in the model. The convergence of the attractors Aµ to the attractor A0 of the averaged equation is also established.

Averaging of equations of viscoelasticity with singularly oscillating external forces

Conti, Monica;Pata, Vittorino
2017-01-01

Abstract

We consider a family of nonautonomous viscoelastic equation with memory and singularly oscillating external forcing, together with the averaged equation.Under suitable assumptions on the nonlinearity and on the external force, the related solution processes acting on the natural weak energy space H are shown to possess uniform attractors Aµ. The family Aµ turns out to be bounded in H, uniformly with respect to the parameters involved in the model. The convergence of the attractors Aµ to the attractor A0 of the averaged equation is also established.
Dynamical process; Equations of viscoelasticity; Singularly oscillating external forces; Uniform global attractors; Mathematics (all); Applied Mathematics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1041095
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