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

IF 0.4 Q4 MATHEMATICS
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))$. Under a suitable conditions, we establish an explicit and general decay rate results of the energy by introducing a suitable Lyaponov functional and some proprieties of the convex functions. Finally, some applications are given. This work generalizes the previous results without time delay term to those with delay.
具有时滞的Hilbert空间中二阶抽象粘弹性方程的一般衰变
本文讨论了一个具有时滞的二阶抽象粘弹性方程和满足$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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