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.
Applied Mathematics and Optimization – Springer Journals
Published: Jun 1, 2015
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