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

Journal Article · Mon Jun 15 00:00:00 EDT 2015 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-014-9266-0· OSTI ID:22469915

Apalara, Tijani A., E-mail: [e-mail] ^[1]; Messaoudi, Salim A., E-mail: [e-mail] ^[2]

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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)

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.

• OSTI ID: 22469915
• Journal Information: Applied Mathematics and Optimization, Vol. 71, 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); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
HEAT FLUX
MATHEMATICAL SOLUTIONS
ONE-DIMENSIONAL CALCULATIONS
POLYNOMIALS
SECOND SOUND
STABILITY
THERMOELASTICITY