Abstract
In this paper, we consider a second-order abstract linear equation with infinite memory and time delay terms. Under appropriate assumptions on the convolution kernel and on the weight of the delay, we prove the well-posedness and the exponential stability of the system. Our stability estimate proves that the unique dissipation given by the memory term is strong enough to stabilize exponentially the system in presence of delay. Some applications are also given.
| Original language | English |
|---|---|
| Pages (from-to) | 507-526 |
| Number of pages | 20 |
| Journal | IMA Journal of Mathematical Control and Information |
| Volume | 30 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 2013 |
Keywords
- asymptotic behaviour
- delay
- memory
- semigroups
- well-posedness
ASJC Scopus subject areas
- Control and Systems Engineering
- Control and Optimization
- Applied Mathematics