On the stabilization of Timoshenko systems with memory and different speeds of wave propagation

Aissa Guesmia (1) , Salim Messaoudi (2)

1 IECL - Institut Élie Cartan de Lorraine
2 KFUPM - King Fahd University of Petroleum and Minerals

In this work we consider a one-dimensional Timoshenko system with different speeds of wave propagation and with only one control given by a viscoe lastic 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.

Domaines: Equations aux dérivées partielles [math.AP]

Aissa Guesmia, Salim Messaoudi. On the stabilization of Timoshenko systems with memory and different speeds of wave propagation. Applied Mathematics and Computation, 2013, 219 (17), pp.9424-9437. ⟨10.1016/j.amc.2013.03.105⟩. ⟨hal-01094943⟩