Abstract
In this work we consider a one-dimensional Timoshenko system with different speeds of wave propagation and with only one control given by a viscoelastic term on the angular rotation equation. For a wide class of relaxation functions and for sufficiently regular initial data, we establish a general decay result for the energy of solution. Unlike the past history and internal feedback cases, the second energy is not necessarily decreasing. To overcome this difficulty, a precise estimate of the second energy, in terms of the initial data and the relaxation function, is proved.
| Original language | English |
|---|---|
| Pages (from-to) | 9424-9437 |
| Number of pages | 14 |
| Journal | Applied Mathematics and Computation |
| Volume | 219 |
| Issue number | 17 |
| DOIs | |
| State | Published - 2013 |
Bibliographical note
Funding Information:This work was initiated during the visit of the second author to Lorraine–Metz University during summer 2009 and finalized during the visit of the first author to KFUPM during spring 2010. This work has been partially funded by KFUPM under Project # SB100003. The authors thank both universities for their support.
Keywords
- General decay
- Memory
- Non-equal wave speed
- Relaxation function
- Timoshenko
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics