当前位置: X-MOL 学术Appl. Anal. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Blow-up result for an abstract evolution problem with infinite memory and time-varying delay
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-12-22 , DOI: 10.1080/00036811.2020.1863374
Houria Chellaoua 1 , Yamna Boukhatem 1
Affiliation  

In this paper, we consider an abstract second-order viscoelastic equation with infinite memory, time-varying delay and a nonlinear source term. To the best of our knowledge, there is no blow-up result of solutions for the nonlinear viscoelastic equation with time-varying delay. Moreover, our result extends the blow-up result obtained for problems without memory term to those with infinite memory and problems with constant delay to time-varying delay. Under suitable conditions on initial data, the kernel memory function and the involved functionals, we establish the local existence using the semigroup theory and we prove a finite time blow-up result for the solution with positive initial energy. We also give some applications to illustrate our main result.



中文翻译:

具有无限记忆和时变延迟的抽象进化问题的爆炸结果

在本文中,我们考虑了一个具有无限记忆、时变延迟和非线性源项的抽象二阶粘弹性方程。据我们所知,具有时变延迟的非线性粘弹性方程的解没有爆炸结果。此外,我们的结果将没有记忆项的问题扩展到具有无限记忆的问题,将具有恒定延迟的问题扩展到时变延迟。在初始数据、核记忆函数和相关泛函的适当条件下,我们利用半群理论建立了局部存在性,并证明了具有正初始能量的解的有限时间爆破结果。我们还给出了一些应用程序来说明我们的主要结果。

更新日期:2020-12-22
down
wechat
bug