TY - JOUR

T1 - Decay property of Timoshenko system in thermoelasticity

AU - Said-Houari, Belkacem

AU - Kasimov, Aslan R.

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2011/12/30

Y1 - 2011/12/30

N2 - We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity-loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L 2 decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity-loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity-loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to U 0∈H s(R)∩L 1,γ(R) with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t -γ/2. © 2011 John Wiley & Sons, Ltd.

AB - We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay property of the regularity-loss type. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We derive L 2 decay estimates of solutions and observe that for the Fourier law the decay structure of solutions is of the regularity-loss type if the wave speeds of the first and the second equations in the system are different. For the Cattaneo law, decay property of the regularity-loss type occurs no matter what the wave speeds are. In addition, by restricting the initial data to U 0∈H s(R)∩L 1,γ(R) with a suitably large s and γ ∈ [0,1], we can derive faster decay estimates with the decay rate improvement by a factor of t -γ/2. © 2011 John Wiley & Sons, Ltd.

UR - http://hdl.handle.net/10754/561966

UR - http://doi.wiley.com/10.1002/mma.1569

UR - http://www.scopus.com/inward/record.url?scp=84856264109&partnerID=8YFLogxK

U2 - 10.1002/mma.1569

DO - 10.1002/mma.1569

M3 - Article

VL - 35

SP - 314

EP - 333

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 3

ER -