Decay properties of linear thermoelastic plates: Cattaneo versus Fourier law

Belkacem Said-Houari

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.
Original languageEnglish (US)
Pages (from-to)424-440
Number of pages17
JournalApplicable Analysis
Volume92
Issue number2
DOIs
StatePublished - Oct 10 2011

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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