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Title: An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of 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.
Authors:
 [1] ;  [2]
  1. King Fahd University of Petroleum and Minerals, Affiliated Colleges at Hafr Al-Batin, General Science and Studies Unit-Mathematics (Saudi Arabia)
  2. King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics (Saudi Arabia)
Publication Date:
OSTI Identifier:
22469915
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 71; Journal Issue: 3; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; HEAT FLUX; MATHEMATICAL SOLUTIONS; ONE-DIMENSIONAL CALCULATIONS; POLYNOMIALS; SECOND SOUND; STABILITY; THERMOELASTICITY