General decay for a viscoelastic rotating Euler-Bernoulli beam

Ammar Khemmoudj; Imane Djaidja

doi:10.3934/cpaa.2020154

Article Contents

2020, Volume 19, Issue 7: 3531-3557. Doi: 10.3934/cpaa.2020154

This issue Previous Article Multiplicity of radial and nonradial solutions to equations with fractional operators Next Article The Hardy–Moser–Trudinger inequality via the transplantation of Green functions

General decay for a viscoelastic rotating Euler-Bernoulli beam

Ammar Khemmoudj^, and
Imane Djaidja

Laboratory of SDG, Faculty of Mathematics, University of Science and Technology Houari Boumedienne, P.O. Box 32, El-Alia 16111, Bab Ezzouar, Algiers, Algeria

^* Corresponding author
^* Corresponding author

Received: February 2019

Revised: January 2020

Published: April 2020

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Abstract

In this paper, we consider a viscoelastic rotating Euler-Bernoulli beam that has one end fixed to a rotated motor in a horizontal plane and to a tip mass at the other end. For a large class relaxation function $ q $, namely, $ q^{\prime}(t) \leq -\zeta(t)H(q(t)) $, where $ H $ is an increasing and convex function near the origin and $ \zeta $ is a nonincreasing function, we establish optimal explicit and general energy decay results from which we can recover the optimal exponential and polynomial decay.

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Mathematics Subject Classification: Primary: 35B40, 35L05, 35L20; Secondary: 93D15, 93D20.

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References

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