Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

Said-Houari, Belkacem

Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

Type

Article

Authors

Said-Houari, Belkacem

KAUST Department

Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date

2011-10-10

Print Publication Date

2013-02

Date

2011-10-10

Abstract

In this article, we investigate the decay properties of the linear thermoelastic plate equations in the whole space for both Fourier and Cattaneo's laws of heat conduction. We point out that while the paradox of infinite propagation speed inherent in Fourier's law is removed by changing to the Cattaneo law, the latter always leads to a loss of regularity of the solution. The main tool used to prove our results is the energy method in the Fourier space together with some integral estimates. We prove the decay estimates for initial data U0 ∈ Hs(ℝ) ∩ L1(ℝ). In addition, by restricting the initial data to U0 ∈ Hs(ℝ) ∩ L1,γ(ℝ) and γ ∈ [0, 1], we can derive faster decay estimates with the decay rate improvement by a factor of t-γ/2. © 2013 Copyright Taylor and Francis Group, LLC.

Citation

Said-Houari, B. (2011). Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law. Applicable Analysis, 92(2), 424–440. doi:10.1080/00036811.2011.625015

Acknowledgements

This work has been supported by KAUST.