General decay for second-order abstract viscoelastic equation in Hilbert spaces with time delay

IF 0.4 Q4 MATHEMATICS Boletim Sociedade Paranaense de Matematica Pub Date : 2022-12-26 DOI:10.5269/bspm.52175
Houria Chellaoua, Y. Boukhatem
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引用次数: 0

Abstract

The paper is concerned with a second-order abstract viscoelastic equation with time delay and a relaxation function satisfying $ h^{\prime}(t)\leq -\zeta(t) G(h(t))$. Under a suitable conditions, we establish an explicit and general decay rate results of the energy by introducing a suitable Lyaponov functional and some proprieties of the convex functions. Finally, some applications are given. This work generalizes the previous results without time delay term to those with delay.
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具有时滞的Hilbert空间中二阶抽象粘弹性方程的一般衰变
本文讨论了一个具有时滞的二阶抽象粘弹性方程和满足$h^{\prime}(t)\leq-\zeta(t)G(h(t))$的松弛函数。在适当的条件下,我们通过引入一个适当的Lyaponov泛函和凸函数的一些性质,建立了能量的显式和一般的衰变率结果。最后给出了一些应用。这项工作将以前没有时间延迟项的结果推广到有延迟项的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.40
自引率
0.00%
发文量
140
审稿时长
25 weeks
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