An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

作者：Apalara Tijani A; Messaoudi Salim A^*

来源：Applied Mathematics and Optimization, 2015, 71(3): 449-472.

DOI：10.1007/s00245-014-9266-0

• Well-posedness
• Exponential and polynomial stability
• Thermoelasticity
• Timoshenko
• Second sound
• Cattaneo's law
• Delay

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo's law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715-2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715-2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715-2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.

• 出版日期2015-6
• 单位中国石油大学（北京）