Skip to Main content Skip to Navigation
Journal articles

Some well-posedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay

Abstract : In this paper, we consider a class of second order abstract linear hyperbolic equations with infinite memory and distributed time delay. Under appropriate assumptions on the infinite memory and distributed time delay convolution kernels, we prove well-posedness and stability of the system. Our estimation shows that the dissipation resulting from the infinite memory alone guarantees the asymptotic stability of the system in spite of the presence of distributed time delay. The decay rate of solutions is found explicitly in terms of the growth at infinity of the infinite memory and the distributed time delay convolution kernels. An application of our approach to the discrete time delay case is also given.
Document type :
Journal articles
Complete list of metadata

Cited literature [52 references]  Display  Hide  Download

https://hal.inria.fr/hal-01281645
Contributor : Aissa Guesmia <>
Submitted on : Wednesday, March 2, 2016 - 2:52:54 PM
Last modification on : Monday, April 12, 2021 - 12:02:04 PM
Long-term archiving on: : Sunday, November 13, 2016 - 6:41:07 AM

File

CPAA15.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Aissa Guesmia, Nasser-Eddine Tatar. Some well-posedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay. Communications on Pure and Applied Analysis, AIMS American Institute of Mathematical Sciences, 2015, 14 (2), pp.457-491. ⟨10.3934/cpaa.2015.14.457⟩. ⟨hal-01281645⟩

Share

Metrics

Record views

272

Files downloads

978