Abstract
It is known that when we add a viscoelastic damping to a frictional damping acting in the domain we might lose the property of exponential stability of the system. Moreover, a necessary condition for a system to be sub-exponentially stable is that the kernel itself must be sub-exponentially decaying to zero. Having this in mind, a natural question to be asked is that of when this necessary condition is also sufficient. We prove that this is the case for a fairly large class of kernels.
| Original language | English |
|---|---|
| Pages (from-to) | 336-340 |
| Number of pages | 5 |
| Journal | Applied Mathematics Letters |
| Volume | 22 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 2009 |
Bibliographical note
Funding Information:The author is indebted to the referees for their valuable comments and for pointing out an error in the original version of this work. The author is also grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through the Grant # SB070013.
Keywords
- Exponential decay
- Frictional damping
- Memory term
- Relaxation function
- Viscoelasticity
ASJC Scopus subject areas
- Applied Mathematics
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