Exponential decay for a neutral one-dimensional viscoelastic equation

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Hacettepe Journal of Mathematics and Statistics
Volume:47 Issue:3
Exponential decay for a neutral one-dimensional viscoelastic equation

Exponential decay for a neutral one-dimensional viscoelastic equation

Authors : Nassereddine TATAR

Pages : 625-635

View : 45 | Download : 10

Publication Date : 2018-06-01

Article Type : Research Paper

Abstract :In this work we consider a viscoelastic string subject to a delay of neutral type. The delay occurs in the second time derivative. Although delays are known by their destructive nature, here we prove an exponential decay result. We shall use the multiplier method and modify the classical energy by judicious choices of other functionals. This would lead to an appropriate differential inequality which allows us to conclude. It seems that this issue has never been discussed before in the literature.
Keywords : Exponential decay, modified energy, multiplier technique, neutral delay, stability

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